Hello, and thank for seeking technical assistance for your Mac .I am Sr. Mac Support Specialist, TD at your service.
This issue you are experiencing, the 3 light pulses on the front panel of the PowerMac G5, means "3 flashes, pause Incompatible memory (RAM) is installed"
Here is the link for PM G5 LED Diagnostics
• LED Diagnostics for PMG5
• I am not sure if there has been any new memory (RAM), installed this could very well be the issue.
• If you have not had any new memory installed, it means the RAM currently in your PowerMac ,may be failing or has failed.
The best advice in a case like this would to take your Power Mac in for diagnostics and repair. Unless you are tech savvy and your PM G5 is no longer under warranty, you can open your PM G5 and reseat the memory and retest your Power Mac's startup. Otherwise, it is best to consider taking your computer in for service.
I have 2 key links here for you, if you need to locate the nearest Apple Retail Stores or Apple Service providers in your area.Apple Retail Store Locator
(Genius Bar)Apple Authorized Service Provider
If you have need for further assistance, please do not hesitate to reply back to this post. Thanks.