BSOD after various activites/new account explorer.exe problem

Hello sevenforums!
I want to start off by saying I come here first to find all my problem solving. But alas, I have a few that couldnt be solved
Any way I have two problems.

First, my computer BSOD's randomly. And when I say random, I mean at the most random times such as just at the desktop, or when I browsing on chrome. I don't know where to find the BSOD info afterword, but I will provide you with it with some directions. I havn't really looked far into this one though, so its not that crucial for an answer.

Problem number two.
I share my computer between me and my brother. We've always used the same user, but we decided to make a new user for us. After we made a new user, I logged off and logged back on. The user had administrative privileges too. On logging in, I was given an error saying about:
Explorer.exe had crashed.(0xc000002)Press ok to close it.
I know a little about computers, so I know explorer.exe is basically the desktop. When I pressed ok, I was taken to the desktop. But the desktop was completely blue with no taskbar. I hit cntrl+shift+esc and the task manager came up. I hit new task and typed in explorer.exe. It came up with the same error as before. I then logged off and onto my other account. I looked up information leading to this. One answer was because I had CA suite on, but I don't: I use Microsoft Security Essentials.(Is that bad?) I would really like a new account, but I just don't know how to fix this. Any help?

Thanks for reading this
Noahster11

Hey, thanks for the quick response.
Anyway: I did a system restore, and tried to create a new account. It did the same exact thing as before.
Is it ok if I undo the restore, as it didn't really solve anything?
Thanks for the link for the BSOD reporter. Next time it BSOD's, I'll report it.
Noahster11