Graphics card burned out?

My Sapphire Hd7750, which I had for i think 5 months, just stopped working. When I started up the computer this morning it went into the bootup screen saying Starting Operating System, then it just does nothing, so i restarted the computer. It booted up fine but it was very slow, after a while I decided to restart the computer, and plug in my hdmi cable to my HDTV. This time after the bootup screen, it goes black, and does nothing with no audio either.
Could this be the graphics card problem?

More then likely yes, try booting from the on board video from your motherboard and see if the same issue happens.
If it works then try resiting the video card and making sure there is no dust in the slot and try booting with it again. If the issue still happens then something is up with the video card or possibly the board but I couldn't say unless you had another video card to test to make sure it's not the motherboard with issues or another computer that is capable of booting graphic cards and has the right requirements. I think more then likely it's the video card having issues.

Thanks for the reply, I have tried to dust the inside of the computer but that didnt work, I also replace the graphics card with another one I had lying around, and now it works. But what should I do with the old graphic card now?

Throw it out?
Use the warranty?