What are these multi-colored cross-hatched lines on monitor?

This has happened occasionally: When first booting my Gateway desktop (DX-4720-03, running W7 HP 64-bit with a Samsung 193P monitor, 256MB (shared) NVidia GeForce 7100 integrated graphics chip), vertical and horizontal cross-hatching lines (many lines of different colors) would appear on the monitor...and there is no response from the comuter. I would then manually turn the computer off and re-boot. On re-booting, the black and white screen gives me various choices on how to open, I choose "open normally," and all is well. But, then again, sometimes on rebooting no safe mode screen and everything boots properly. Other than that, I have had no problems with the computer or monitor's functioning (but recently the monitor's DVI connection crapped out and I'm now using VGA connection...which is working fine). Two suggestions have been made. One says that my GPU may be overheating. I doubt that as the cross-hatching only appears when the computer is freshly booted (ie, has been off for a long time, like overnight), never while running. The other suggestion was that my graphics chip could be going.