I have a Power Mac G5 quad core (2006) and it does not work.

You have a PowerMac, not a Mac Pro. I requested that yur posted be moved to the PowerMac forum,

Power Mac

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.

http://support.apple.com/kb/HT1547

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, should be the 1st one ..

http://eshop.macsales.com/item/Newer%20Technology/CR2032/

http://eshop.macsales.com/item/Newer%20Technology/BAA36VPRAM/

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

https://discussions.apple.com/thread/2620983?answerId=15499912022#15499912022

https://discussions.apple.com/thread/3175959?answerId=15613068022#15613068022

https://discussions.apple.com/thread/3270112

https://discussions.apple.com/thread/3287993?answerId=16053892022#16053892022

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

I think it needs the hair dryer or heat gun thing, bit I've never really understood the "on some computers the power LED will flash a corresponding number of times plus one" statement.

Anyway, seems a RAM/Memory problem, might pull the RAM & clean the contacts with a rubber eraser, try one Pair at a time if you have more than one pair..