2010 Macbook pro freezes a lot, but mouse still moves. It unfreezes if you wait. It also hard crashes... Also, weird lines and screen flashes.

Question

I have a 2010 Macbook pro running snow leopard (Mac OS 10.6.8).  First off, this has been the worst computer I've ever owned or have heard of someone having, Mac or PC.  There hasn't been a time where something hasn't been wrong.  I'm going to list my specs, my current problems and maybe list previous problems after that.  Any advice or suggestions would be great.  My brother works for apple out in Cali and I've been sending him crash and bug reports and he can't seem to figure out what's going on.
Specs:
2010 Macbook Pro (Mac OSX 10.6.8)
Processor: 2.66 GHz Intel Core i7
Memory: 8 GB 1067 MHz DDR3
Graphics Cards: Intel HD Graphics (288 VRAM) and a NVIDIA GeForce GT 330M (512 VRAM)
(if you want more info, just ask)
To start things off, my computer hard crashes at random points playing basically any game.  StarCraft 2 (when I could play the game prior to Blizzard patching my OS out of the minimum requirements), League of Legends, MineCraft and others all crash while in use.  My computer screen suddenly flashes white and then to black and whatever audio may have been playing in the past second of gameplay is thrown into a constant loop.  The screen is solid black with no mouse and there is no keyboard functionality.  The only thing I can do is hold down the power button.  I first started noticing this problem back when StarCraft 2 Heart of the Swarm came out.  I would crash every 4 or 5 games in this way.  Since that was happening I resorted to playing other games such as League of Legends.  I wasn't having any trouble at all, but gradually it started to have the hard crashing issues.  Initially every handful of games, now it crashes in roughly 50% of the games I play.  This happens while I have NO other applications open and this has happened even after a complete restart with only 2 things opening at startup.  League started crashing in this way after I brought my computer in to have a fan replaced. 
Another thing which has started happening since I had my fan replaced at the apple store: My computer has become very sluggish at times and my computer freezes in another way.  Many times a day, I will find I click on something in an application and the entire computer locks up.  There's no spinning beachball.  There's no movement of any sort on the screen and there is no button functionality, but I can move the mouse.  Clicking does nothing.  This sort of freeze lasts for about 30 seconds up to 5 or 6 minutes or so.  After that, it suddenly just decides to work again.  I can tell when it unfreezes because the clock in the corner jumps to the correct time.  This has happened frequently while using Google Chrome, Firefox and Safari.  It also happened while trying to use Skype.  It was freezing the most when facebook or youtube has been open, but it happens without that happening as well.  One of the first times I noticed it, earlier this year, I was searching for work and tried to go to this website: http://www.nhab.org/ (looking for a job).  It froze my computer as I described above (and I didn't know it would unfreeze after several minutes, so I thought my computer was completely frozen). I restarted, went to the same website and it froze again.  I did this a third time and it froze again, so I restarted again.  On the fourth try, it loaded.  The frequency of this problem is ridiculous.  I actually decided to delete Google Chrome from my computer (and its support files) since my computer would freeze the most often with Chrome (though I used Chrome mostly for youtube and watching tv shows online).  Almost instantly after deleting Chrome, my computer was running significantly faster.  things loaded quicker in other browsers and aplications loaded smoother.  My text no longer lagged when typing in facebook...  It hasn't solved the freezing, though the freezing tends to last less time now.
Another thing that happens, which I am not sure is normal: When my computer is booting, after the grey screen, it changes to light blue.  During this light blue time, often times white horizontal centimeter to inch wide bars will flash across the screen near the top.  This also happens on shutting down.  I also noticed that when it shuts down the screen doesn't just shut off.  The screen flickers quick for up to a second and then it is off.  It doesn't just turn off.
My computer has also occassionally flashed for a brief fraction of a second, to the blue start up color and back to whatever I am doing.
Those are all issues I am having right now and I am beginning to wonder if this several thousand dollar computer is capable of doing much more than just writing text..
Prior issues I have had:
Right from the start, I have had major graphical issues which I showed to the people at the apple store and they reinstalled flash, but they really didn't know what was going on.  These glitches would tiles previous graphical things I had done in an artistic mozaic across my desktop, replacing my background image with broken mozaics.  It's hard to explain without showing, so here are 2 screenshots from it:
The people at the store thought it was just flash... but I don't understand how that could be flash.  I would have to flip through different desktop backgrounds I used to make it go away.  After it doing this for 2 years, it has only happened once since then and not very badly..
Another issue I had: The battery on my laptop just about exploded... I woke up one morning with my laptop sitting on my night stand as usual, but there was a small crack across part of my trackpad.  I was scared because I thought I must have done something... I went to the bathroom, took a shower and when I came back the crack was farther across the trackpad.  I had breakfast, came upstairs and my trackpad had 1 crack across the whole thing with multiple mini cracks going in every direction from it.  After telling my brother what was going on, he quickly said that it was the battery and to take it to a store.  I took it to the store and showed them what was happening and they very quickly took it out back and I quote "threw the battery in a firesafe immediately" because when they opened the laptop it started to quickly expand.  This ended up cracking my trackpad as well as bending the bottom of the body on the laptop.  All had to be replaced...
Then I had the fan sounding like a weedwacker, so I had it replaced a couple months ago and a couple months ago is when the freezing began, the computer started running slowly and all games crash the computer.
I have had a lot of things go wrong, not a lot of things go right and I'm really frustrated.  Can anyone tell me how to get my computer to stop freezing or how to make it stop hard crashing during any of the games I play?
Basically, what I have done so far is reset the PRAM I think?  I held command + option + P + R on start up and had it chime 3 or 4 times.  Other than that, I don't know what to do.... suggestions?

Answer 1

I just wanted to follow this up by saying that you were entirely correct in your diagnosis of the situation.  My computer did have the faulty part you linked to.  I brought my laptop in and specifically told them to run that test, had it fail and then argued with the person at the genius bar and the manager.  Eventually they offered to have it sent out and have everything replaced for free of charge.  They did so mainly because I had complained about graphical issues almost every other time I had come in with problems and no one ran the test.  They should have caught this problem during my warranty, but they didn't, even though I mentioned the problem.
Anyhow, after having the part replaced, I haven't had my computer crash a single time since, or had many of the issues mentioned above.  I've never had this experience before.  Even brand new, I got occasional crashes.  Hopefully this new trend continues.
I do find that web browsing is still incredibly slow.  Web browsers just chug along at a slow pace, even though I have great internet speed.  Maybe I'll try just deleting my web browsers and reinstalling them...
Anyhow, thank you for your help and knowledge Clinton.