Power Mac - Video problem

I have a PowerMac G5 with dual 2.5Ghz processors and 3 Ghz of memory. I have had the computer for a few years and have had no problems with it until now.

I booted the computer and the fans were running at full speed. The computer was acting normal other than the fans for about 5 min. Then the computer went into what appeared to be sleep mode and then woke right back up again. It continued to go through this cycle (asleep, awake, asleep, awake) until I shut down. I then tried to reboot and the computer would come on (fans on, power light on, hard drives spinning) but the monitors would not come on. I then forced the mac to shut down and tried rebooting again. The same problem happened. I tried resetting the PMU and after plugging the power cable back into the tower the power light came on but the mac would not power up. I did not have to press the power button to get the power light to come on, just plugged the power cable in. Nothing comes on either, just the power light comes on. I tried holding the power button in to get the light to go off or to get the mac to boot but with no luck. I then decided to check the battery. I took it out and it is reading 3.689 volts so I put it back in. This time the computer booted up. It came up a bit slow but without any problems. That is until about 5 min. went by and the same problem started all over again. Fans kicked into high gear and the computer started cycling from sleep mode to waking up over and over all by itself. I shut down and tried rebooting and again the power light comes on, the hard drives spin and the fans kick on but no display. I found that if I wait about 20-30min. and reboot it will come up just fine but the issues start over again after about 5 min. or so.

I have made no changes to the system in many, many months and have not had any problems at all. The unit is not connected to the internet either. Any suggestion would be greatly appreciated! Thank you.