Trying to understand exactly what happened…
A key got stuck UNDER your laptop keyboard? And you used a nail file to get it out? And now the entire laptop won’t turn on?
Likely what happened, in that scenario, is your laptop does not have a protective layer between keyboard and the motherboard/actual parts inside, or the layer is thin. In that case, you may have damaged one of the sensitive components getting the key dislodged. I would NOT recommend best buy. They really have no idea about what they are doing and will hire nearly anyone who thinks they can repair a PC. I had someone call once because Best Buy told them they had to buy a new computer, because it was cheaper than repairing it. When asked what the issue was, she said she had a virus. A virus and they wanted her to buy a whole new computer (which they could sell her, just come take a look at our computer selection). 10 minutes on the phone with her and her problem was fixed, free of charge, she did it herself with just a little guidance. They are some of the most crooked PC repair people I have ever been around.
Now, a problem finding a good place to take your computer is … a lot of the repair guys are crooks simply because they CAN get away with it in 90% of the cases. If you have a friend who is good with computers, have them recommend a place. If not, try to find a small shop that will take in laptops and look up reviews for it online. Though, again, because they get away with it most the time bad reviews don’t happen. I used to make a lot of money repairing computers and nearly every one of my customers were shocked at how fast I did stuff and how little I charged for it, how few pieces needed replaced, etc. They were willing to just throw money at me to fix whatever I said needed fixing.
Before you hand your laptop over to anyone, get a price quote. No point spending more than the computer costs to repair it, after all. 