Weird lines/dots around cursor

My old Mac Pro - 2x2.66 Xeon, 4gb memory, 3x500gb disks, uses external Apple monitor 20" or so - has been acting weirdly. Was getting stuck at grey screen when starting up.

We went through all the Gray screen appears during startup troubleshooting: removed peripherals - no luck; tried safe mode - no luck; reset PRAM/NVRam - no luck; wiggle all the cables - no luck; tried safe mode again and it booted but there was a very odd pattern around the cursor:

Photo should be visible at this link

The dots and lines in the square varied considerably from few to many in an apparently random pattern - this makes me think video RAM is possible broken? The machine won't boot into hardware test mode so I'm not sure how to test this hypothesis though.

I know it's fairly old and very well used, but financially replacing it right now would be über-difficult so I'd be really happy if it'd last just another year ... any suggestions??

Ricky