I started getting blue screen errors on my laptop. I have tried almost everything possible to fix it myself

Hi, I bought a Toshiba Satellite M55 about 4 months ago. Two months ago I started getting blue screen errors, and every time it would say it was my video driver. I sent it back to the manufacturer twice, they have replaced my hard drive and my motherboard. It worked fine for about a month, and then, of course, about two weeks after my warranty is up I started receiving the blue error screens again. I have tried almost everything possible to fix it myself. I was finally able to update the ATI driver from X200 to X1300, and it seems to be the best solution I have tried in that it will stay on for a day or two without it being turned off due to the blue error screen (before I was getting it nearly every half hour if I was able to get it to turn on in the first place). It will go through maybe a few hours of receiving blue screens constantly, and then it will be fine for another day or two before I receive anything again. I’ve tried updating my bios, but I cannot update it any higher than version 1.80.
Here is just some other information, just in case it helps. It seems to run fine in safe mode, and before I was able to update my video driver if I turned down the screen resolution and coloring it would stay on longer before getting the blue screens. Occasionally the screen will flicker and then simply black out, or it will just freeze all together. Occasionally I will get a blue screen but the computer will shut off within a second of it flashing on the screen and then it will automatically reboot without me having to do anything. After receiving the blue error screen and trying to reboot the system it will take several tries to get it to boot up and then stay on. I also had problems downloading the new driver even though I followed the instructions given to me (after uninstalling the old driver and then trying to install the new one I kept getting messages saying the download was not complete b/c I do not seem to have a VGA display), but after about a day or messing with it I was finally able to get it to download properly.
Any other suggestions on what the problem could be? It was suggested to me that it could simply be my video card, but I do not want to replace it until I know for sure that that is the problem.

Yep, it could be a failing video card, but unfortunately on this model the video card is integrated into the main board and if the video goes bad, you’ll have to replace the entire main board.
I think it also could be a failing memory module. Here are some points that made me think that way. You said that after Toshiba replaced the system board, you still getting the same blue screen errors. Is it right? In my opinion, it’s unlikely to get the same blue screen error with two different motherboards, so it could be not the system board (video card) problem. This model implements dynamically allocated shared graphic memory. What if a part of the memory that is allocated for the video memory is failing?
Here’s my suggestion. Download and run Memtest 86+ utility to test the laptop memory, make sure that the memory passes the test for a few times. Reseat the memory module, just remove it from the memory slot on the system board and put it back. If you have only one memory, most likely it’s installed into the slot located under the keyboard (step 13). You’ll have to remove the keyboard in order to reseat it. If you have two memory modules, remove them one by one and test the laptop after remove each module. If the memory installed in the slot A, try moving it into slot B. (it’s possible that one memory slot is bad and the laptop work fine if you use the second slot). That’s would be nice if you can find a spare memory for test.
Also, I would remove the modem and the wireless card and test the laptop without them.
I don’t think that’s a software problem, because you mentioned that sometimes the laptop will not boot at all. You still should be able to turn on the laptop and get a video on the screen even if the hard drive is completely blank or not installed at all.