I'm don't think it's the driver's problem. The BSOD stated that it was caused by volsnap.sys but the System File Checker didn't find anything wrong. Is there a way to replace the volsnap.sys? And this certain BSOD only seem to appear when I game and Skype at the same time.
Blue screen programs can only give an answer from the information it has been given. If there was a program that could tell you exactly caused the problem then there would be a program that would fix it for you.
The person that develops those programs will be able to retire.
The current programs just give us clues and every once in a while it will give us the answer.
volsnap.sys is Windows Volume Shadow Copy Driver, if SFC didn't find anything then it may be caused by another driver or hardware.
Updated driver. Funny thing happened when I opened Skype; BSOD hit me. This time it's SYSTEM SERVICE EXCEPTION. I'm still wondering why it only happens when I use Skype.
Uninstall Skype and test for stability, if stable then re-install Skype. If it still is a problem you need to find a previous version of skype.
I can't do the long generic scan since it takes like 5 days to scan and I can't do the DOS version scan since I don't have anything to boot from. Is there anything else I should do?
If it takes 5 days then you have a problem.
Testing hardware can be time consuming, now you know why computer shops charge so much for working on computers.
These tests are crucial and need to be completed, if you don't have the time or patience then you should consider taking it to a computer shop for tests.
Run the SeaTools long generic until it finishes, with a 1.5TB drive it will take a while, possibly 12 hours or more. The previous Crystal Disk info is showing some errors, SeaTools may be able to repair the problems and this, of coarse, will take longer to complete.
You mentioned you don't have anything to boot the DOS SeaTools from, get a CD or DVD, better to put it on a USB memory stick.
SeaTools will run faster from DOS as the Windows OS will not be running.
Let us know the results or if you have any questions.