No BSOD - just a blank, black screen...

Downloaded a virus into my computer 2 weeks ago - ran Microsoft Security Essentials to scan & clean.
Downloaded microsoft updates this week, computer froze so I shut it down. Now it won't even reboot........
I am hopelessly illiterate when it comes to this sort of stuff - is it time to dump this computer? It was a rebuilt system to start with......
 
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