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
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
Those in Ephesus. 6 And when Paul had laid his hands on them, the Holy Spirit came on them, and they began speaking in tongues and prophesying.
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. 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.
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?
As for Barnabus and Paul, yes the prophets and teachers laid hands on them but it doesn't say they gave them spiritual gifts.
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. 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".
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.” 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.
That's my understanding of the bible telling me how someone gets spiritual gifts.