Sounds like either the video card..or the mobo (if using onboard video). Could be a bad connection or cable from comp to monitor/television. Will it boot in safe mode (pressing f8 while booting).? Agree with above post. Dust will definitely cause overheating and if you can get in the bios....check voltages/temps if the bios has those capabilities. Another possibility is the resolution to the monitor is set wrong. If the hard drive is still good...you can usually pull it from the desktop and buy a sata/ide to usb connector ( about 12 dollars )that you can hook up to a working comp and transfer all your pics and documents to the good computer.
Now that the fellow geeks have come out of the woodwork, I have a situation. Elderly neighbor's husband passes away. He has every password written down except the Win 7 log-on. She wants to be able to use the PC, not have the files pulled off the HD. To try and crack the password I've tried all of the following. None have worked.
Ophcrack (Vista/7)
Trinity
Offline NT Password and Registry
Kon-Boot
Win 7 repair disc.