No, no. That's not how it works at all.
Once you buy a game through steam, it's yours. You can download it to any computer you want, as long as you're logged into the account you bought it with.
If my steam name was aerowyn, and I bought TF2, I could install it on my laptop, on my PC, on my friend's computer, whatever. But I can only play it if I am logged into MY steam account. Just because it's on my friend's computer does NOT mean that my friend can play it. They'd need to be logged into an account with TF2 credited to them.
Make sense?
So asylum, if you've already bought the game but you can't get it to install, I suggest you take that to the Steam support section at https://support.steampowered.com/ or hit up the Steam forums and ask there.
But if you illegally downloaded the copy of TF2, sorry, but you're SOL.
I don't have any other advice for you.
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