That crossed my mind, but the fans don't spin at an accelerated rate before the computer crashes.

I ran the machine with the side panel off for a bit earlier in the week (leaving the plastic air guide/shield in place). All fans were spinning nicely.

I need to get the G5 up and running since I sold my Windows RAID server over the weekend. Throwing more memory at it seems like my best option right now. Since it's just DDR, there are a lot of other places it can be used if it turns out the memory in the machine is fine.

The good news is that the VNC server built in to 10.5 appears to work nicely.