If you don't mind, maybe you can help me to understand why you believe we still have spiritual gifts today by helping me with how I misunderstand what the bible is telling me.
I think a logical place to start would be how does someone receive a spiritual gift. This is what I see the bible telling me then I will address your counter arguments.
By the laying of the apostle's hands:
6 These they set before the apostles, and they prayed and laid their hands on them.
This is the seven and we see evidence that they received spiritual gifts.
The apostles laid hands on the seven, apparently in connection with their service role of caring for widows. Paul and Barnabas laid hands on church elders also. Stephen and Philip did miracles later, but it doesn't say whether this had anything to do with the apostles having laid hands on them.
The Bible is very clear that spiritual gifts could be given through the laying on of the apostles' hands or without the laying on of the apostles' hands. In Acts 19, Paul lays hands on some men after they are baptized and they spoke in tongues and prophesied. But God had been empowering men to prophesy for over 1000 years before any of the twelve apostles, or Paul or Barnabas, were born.
In Acts not only did the Gentiles in Cornelius' house speak in tongues most likely without Peter laying hands on them, but Paul actually received grace and apostleship without the laying on of hands of the apostles and also did miracles, and laid hands on others and imparted spiritual gifts. Timothy received a gift through Paul's hands. He also received a gift through prophecy, accompanied by the laying on of hands of the apostles.
Ananias laid hands on Saul/Paul. He said he was sent that Saul might receive his sight and be filled with the Holy Ghost. He baptized Saul, and some time later, Saul was an apostle and did miracles. He wrote of apostles in Jerusalem that they that seemed to be somewhat added nothing to him, so that argues against the idea that he recieved a gift, even apostleship, through the laying on of hands of the apostles.
18 Now when Simon saw that the Spirit was given through the laying on of the apostles' hands,
Peter didn't have to address Simons request because he had a bigger problem, for your heart is not right before God
He had no part in that matter because his heart was not right before God. He thought he could buy the gift of God with money. Peter didn't tell him he couldn't do it because he wasn't an apostle, but because his heart was not right before God.
You are correct, Paul does say about Timothy 14 Do not neglect the gift you have, which was given you by prophecy when the council of elders laid their hands on you.
If he hadn't told us For this reason I remind you to fan into flame the gift of God, which is in you through the laying on of my hands, then I would agree. In a situation like this, I would look to harmony of scripture and say Paul gave him the gifts.
Let's stick with what the text says... gift in the singular. There was the gift that was in him through the laying on of Paul's hands, and the gift that was given through prophecy, with the laying on of hands of the elders. If it were theologically significant for us to know that it was the same gift, why doesn't the scripture say so, and why two different ways of the gift being passed to him if there were only one way.
For arguments sake, if elders could give gifts, then there would be a supporting scripture of an elder giving someone a gift that an apostle hadn't laid hands on.
Neither apostles nor elders could give spiritual gifts. They can lay hands on people. I Corinthians 12 teaches that gifts are given as the Spirit wills. If they are laying hands on someone regarding a specific ministry, they can commend them to the grace of God. It may be apostles were moved to lay hands on an individual in regard to a certain gift, or the gift could be specified by prophecy.
The Spirit spoke when Barnabas and Saul were to be separated to the work.
11 For I long to see you, that I may impart to you some spiritual gift to strengthen you—
Why does Paul need to come to them to give them a spiritual gift if an apostle isn't required?
Spiritual gifts can be imparted by the laying on of hands of apostles. Spiritual gifts can be given 'as the Spirit wills' apart from the laying on of hands of the apostles.
Paul tells the one who speaks in tongues to pray that he may interpret (I Corinthians 14:13.) He does not say to pray that an apostle will come to town and lay hands on you so that you may interpret. It would be odd for Paul to tell the Corinthians to eagerly desire spiritual gifts, especially that they may prophesy if there was no chance they could do so if the apostles hadn't laid hands on them specifically to prophesy.
Now to Cornelius. If you don't see Cornelius as a special situation then I will need a good explanation of why not in order for me to put any value in what you tell me. I will lay out why Cornelius is a special situation. They received spiritual gifts directly from God for a specific purpose. To prove, to the Jews, the gospel is for Gentiles and they are to be included as God's people.
Maybe God cared about Cornelius, too. His alms had come up as a memorial before God. You can choose one aspect of the story and say that is THE exclusive purpose of the events... just because you say so. But that method is just a way to eisegete one's own opinions into the passage. All scripture is profitable for doctrine. This passage shows pretty good evidence of a spiritual gift being imparted without the laying on of hands of the apostles. In fact, two of the three passages that mention speaking in tongues in Acts do NOT involve the laying on of hands of the apostles. You are trying to piece together a doctrine that says that gifts are exclusively passed through the laying on of hands of the apostles, but then you have to make out the various examples and statements that don't fit as exceptions.
Other than the apostle Paul, there is no other conversion that is like it nor comes close to being as detailed before or after Cornelius. There is a complete, long, chapter devoted to it and it's talked about in 2 other chapters. There is also a vision involved.
There are only 2 times God directly gave someone spiritual gifts as evident by speaking in tongues and each was a special situation. The apostles on Pentecost and Cornelius. Each time they are referred to, it's called "baptized WITH the HS".
So how many specific stories do we have of conversions of individuals in Acts? I can think of five off the top of my head, Sergius Paulus, Lyddia, the Philippian jailer's household, and the two you mentioned. And two of those are 'special cases.' Given he percentage of 'special cases' in scripture, maybe we should just conclude that God can do 'special cases', and not base doctrine on the idea that God normally does non-special cases without any scripture at all to back up what a normal case is supposed to be like. Sergius Paulus and the Philippian jailer were converted after seeing supernatural events, so are those special cases or normative cases?
Have a look at Acts 11:16 in an interlinear. The word translated 'with' there is 'en' in Greek, and often translated as 'in'.
The apostles:
4 And while staying with them he ordered them not to depart from Jerusalem, but to wait for the promise of the Father, which, he said, “you heard from me; 5 for John baptized with water, but you will be baptized with the Holy Spirit not many days from now.”
But the Greek word is ἐν (en) so often translated as 'in'.
And we know that they received the HS directly from God evident by the speaking in tongues.
Cornelius:
We know that they received the HS directly from God and it was evident by speaking in tongues. When Peter later tells this account, this is what he says; 15 As I began to speak, the Holy Spirit fell on them just as on us at the beginning. 16 And I remembered the word of the Lord, how he said, ‘John baptized with water, but you will be baptized with the Holy Spirit.’
If Cornelius isn't a special situation, then all you have to do is point out another conversion where they received the HS directly from God and it was evident by the speaking in tongues.
Since there are only three cases of speaking in tongues in Acts, and you believe that two of them were cases of receiving the Holy Spirit directly from God, why would you conclude that receiving directly from God is not normative?
That verse in Luke comes to mind, about how if ye then being evil know how to give good gifts unto your children, shall not the Father give the Holy Ghost to them that asks Him.