Hi Grant, seems several problems...
The thermal paste on the CPUs likely needs replacing after this length of time...
Can you count the beeps or flashes?
1 beep = no RAM installed
2 beeps = incompatible RAM types
3 beeps = no good banks
4 beeps = no good boot images in the boot ROM (and/or bad sys config block)
5 beeps = processor is not usable
In addition to the beeps, on some computers the power LED will flash a corresponding number of times plus one. The LED will repeat the sequence after approximately a 5-second pause. The tones are only played once.
Note: In this case, a flash is considered to be 1/4 second or 250 ms or greater in length.
If you're sure the RAM is good, try the Hair Dryer trick...
http://discussions.apple.com/message.jspa?messageID=13240047#13240047
https://discussions.apple.com/thread/3061091?answerId=15223603022#15223603022#15223603
https://discussions.apple.com/thread/2620983?answerId=15499912022#15499912022#15499912
https://discussions.apple.com/thread/3175959?answerId=15613068022#15613068022#15613068
https://discussions.apple.com/thread/3270112
https://discussions.apple.com/thread/3287993?answerId=16053892022#16053892022#16053892
No power light at all...
https://discussions.apple.com/thread/3692775?tstart=0
It can show on any G5, and even many other computers & electronic devices of the period.
http://www.macintouch.com/reliability/pmg5.html
http://lowendmac.com/ppc/power-macintosh-g5.html
And see this last one in particular...
https://discussions.apple.com/thread/3507385?answerId=16781690022#16781690022
Heat gun better...
https://discussions.apple.com/thread/3916312?tstart=0
Might be time to replace the PRAM Battery, 4 years is close to their lifespan, far less if ever without AC power, & can cause strange startup problems...
See which one your G5 has...
http://eshop.macsales.com/item/Newer%20Technology/CR2032/
http://eshop.macsales.com/item/Newer%20Technology/BAA36VPRAM/