Yes, capacitors are usually the issue with iMac G5's. What you're describing doesn't sound like a battery issue to me.
Unfortunately my experience with iMac G5's is very limited. Hopefully someone else who knows these machines better can chime in here with some advice for you.
It would be helpful if you could describe what you mean by "It will boot up first thing in the morning, but usually not again." For instance:
- Does this literally mean "in the morning" or just after some period of inactivity? I can't imagine an issue that would restrict a Mac's operation to a particular time of day, unless somehow a system setting has changed.
- When it does boot, does everything appear to progress normally in your experience?
- Is there anything unusual occurring during startup?
- Unusual sounds, images on screen, artifacting, anything?
- When it does boot, is it taking longer to boot than usual?
- Do you get the Apple "bong" sound on startup?
- When it won't boot, what happens?
- Does it respond at all, or just refuse to power on?
- Does it begin a boot sequence, and just fail to complete?
- Do you ever get a screen that looks like this:
- When you do get it functional, how long does it run? Is it always the same amount of time?
- When it stops working, what happens?
- Does the iMac just power off?
- Do you get a black screen but it stays on...e.g., you can still hear fans running, etc.?
- Does the screen remain normal, but the computer "freezes up", i.e., becomes unresponsive?
- Does it go into a kernel panic (screen that looks something like the following):
I'm not trying to be nitpicky, but any further info you could provide will help someone troubleshoot your problem.
Alternatively, you could just go buy a FireWire cable, boot the bad iMac in Target Disk Mode and see what happens. Maybe it will stay running long enough to get that fonts folder transferred over. Or, why not move the fonts folder onto a USB flash drive and transfer it that way?