Powermac G5 start-up issues

Hello,
My Powermac G5 refuse to start normally: sometimes, it boots perfectly, sometimes it doesn't.

Switch on the G5: fans spin, no chimes, no keyboard, no video, fans accelerate few minutes after...I can just push the power button to switch off the G5.

So, I clean up the G5, disconnected firewire matérials, ram, replace it, disconnected video card, hardrives, I bought new pram battery. Nothing changes.

But, when it starts, the Mac is fully fonctionnal...

Please someone help me ?

Thank you for your answers.

Is it random or on cold boot only?

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Yes, it's random. There is two days ago, in the evening, it start up 3 times.
Yesterday, it can't boot...the white front led illuminate, but no boots.

Did you notice one CPU disappear when it starts and works (if it's DP ofc)?

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I don't know how to do to get this information. Can you explain more about this, please?

I have noticed that g5s don't like soft boots. I disable sleep mode and only shutdown then start up.

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Sorry, but what is soft boot?

Another point I used to get, I don't know if it's very important for G5 trouble, I try to explain :

For example, I'm running with leopard 10.5.8, and I want to quit/restart.
2 choices: reboot, or shut down.
- With shut down, no problem.
- With reboot option, it will crash on start up, with black screen, no chimes, no video, like the big problem in this subject.
If I want to reboot, I must to shut down, then switch on the G5, after waiting few minutes.

Sorry, I hope someone understand..

OK, thanks, now it's hard to see "about this mac" section, because it doesn't start everyday .. I need to be lucky

Just video card, would be a great news !
Do you think I may replace video card first?

I guess this is AGP 8X video card (?), can you suggest a video card or where to find a nice one somewhere? On eBay? It's for music editing.

Some news from my Powermac G5:

today I was able to copy data with my iBook G4, and firewire cable.
I moved the graphic card (it seems to be ATI Radeon X800XT, but I'm not sure) and reconnected it.
The G5 started and ran all the afternoon.
This evening I shut it down, and when I wanted to start it, no response again ...

Please can you advise me video card I have to buy, because a friend tells me the motherboard's bios can make trouble with some video card.

Thank you.