is my graphics card broken

sound more like a power or a heat issue. i would start by seeing if all the fans on the gpu and cpu and moving and there not covered in dust.if it still hangs if your pc has ipgpu (cpu or onboard video chipset). turn the pc off and unplug the gpu and see if the onboard video is fine. if you dont try swapping the video card to another pc or see if another video card works fine in the pc that having issues. if a replacment card does the same thing then it a power issue.

Could be a lot of reasons, on the blue screen theres an error code. Do you remember what it is? If you find that code you can google it or post it on here and it will give you the reason for the blue screen.

More known as a STOP code sorry about that.

my onboard graphics works fine but everytime i put my graphics card in then it does the same thing...so i gues its my graphics card thats "dead" ...im going to buy me a new graphics card so mmmm thanks guys for the info...i now know something new...

no no no... as smorizio said, it could be your psu. Don't be so quick dumping you gpu. Usually when the gpu kicked the bucket, you will see artifacts on your screen, but will not causing your system to restart.
Your onboard's fine because it drew less power from the psu, that's why it run ok.

mmmmmmm didn think like that...make sense to me now cos i had that problem with my graphics 3 years ago...and you right if it my graphics then the pc wont restart...will test the card onother p thanks man

Yeah thats what I was recommending, borrow or buy another card and see if it was just the card the was defective. If it does the same thing then I would say thats its probably a PSU issue.