What is wrong with my Macbook Pro? (distorted screen, beeping, slow)

I have a late 2012 Macbook Pro (13-inch) that I got from Best Buy. It worked perfectly fine for a year, but then went crazy.

First, it started shutting down here and there, and icons bounced a lot in the dock. Then, one day, I googled something and it froze, then flashed a strip of multicolored barcode-like lines. So, I shut it down and it overheated then began to beep 3 times and flash a light.

I brought it in and they just wiped the hard drive. Then, it happened again while I was watching a video only a short time later. I was going to re-seat the RAM myself but the inside of the computer looked all messed up. I took it in and they gave me a new LCD but it has a dead pixel now. It worked fine for 1 month after that.

Then, I was using the laptop on my bed and it shut off randomly a couple of times while I was on Facebook and started beeping. I rebooted it and tried to fix it but it happened again the next day. I brought it back to Best Buy and they said it was hot and sold me a $20 cooling pad.

That worked for a few days, then I was watching TV online and it happened again. I brought it back to Best Buy and they replaced the RAM. Now, I was watching something online and it happened yet again. I was able to reboot and it worked okay now for a couple of hours but it did freeze again and I had to shut it down.

Everytime I go to Best Buy, they tell me "If we have this issue 1 more time, we will replace your computer." But, then, they say the same thing every time and that it's their policy. I have paid for Office now and only have 1 download left. Also, this is ridiculous because I'm a student and I've had my Mac gone for 2 weeks at a time at least 3 or 4 times. When this happens, I get stuck using my iPad and can't use flash so I've spent tons of money of apps for flash and other things to make my iPad functional.

Can somebody just tell me what's wrong with it? It "passes the hardware test" every time and the Geek Squad keeps asking me stupid questions like "Did you check your internet connection and reset your modem?" When I asked them the first time to do a PRAM test, they didn't know what that was and asked me to go on iTunes or clear my cache or something like that.

I have had a bad experience with them altogether. I got my Macbook for $500 because I had a PC before that I paid $700 for and it eventually broke. They were unable to repair that one because the hard drive had failed, although they had previously been convinced that I needed to uninstall my Norton to fix that problem.

Sorry if I'm ranting, but my Macbook is like a child to me (not to sound weird) and I'm sick of this problem. It's working fine at the moment but I know this will happen again randomly like always.