Problems (power, network) with PowerMac G4

A couple of days ago I started having serious problems with my PowerMac G4.

The first thing that happened was that it sort of froze. The clock kept ticking, and I could move the mouse, but all apps gave a spinning beachball of death.

So I did a hard restart.

When the machine booted again, the clock was set to December 1969, which it gave me a warning about, and I set it to the correct time. I figured my battery is dead. More troubling was the fact that I couldn't connect (via wired ethernet) to my network. In fact, the light on the router that shows a physical link with a machine didn't light up.

Since then I've zapped the PRAM and rebooted a few times. I believe one of these times the clock change stuck, but the rest of the time it went back to 1969.

It also was taking a loooooong time to boot, I would guess 5 minutes. It spent a long time on an empty blue screen.

I just tried installing an ethernet PCI card, thinking that my battery and my ethernet port might have both died at the same time somehow, but now I have a new problem. Before Finder was done starting up, the machine just powered off all of a sudden. After that I couldn't get it to boot at all. I'd press the power button and the light would flicker but it would just die again instantly. I let it sit for about an hour and tried again. It spent a minute or so trying to boot and then powered off again. Now I'm having the same problems starting it up.

Any ideas?

 

The clock was my first clue, but I haven't had a chance to go buy a new battery yet. And I didn't think that the battery would affect my ethernet like that...