Power Mac :: G5 Boots Sporadically & Doesn't Remember Date And Time?

I have an old Dual 2.5 GHz PowerPC G5 (aluminum tower). When it boots up, I get a message that the Date & Time are no longer correct. I go into date and time settings and reset them, however when I shot down and reboot later, the time has been reset to June 1969 or some similar date. Also, when the computer shuts down, it cannot be rebooted immediately. If I try to reboot it, I hear the fans start up and drives start spinning, but then they all seem to power down (a red light can still be visible inside. If I shut it down and wait 15 minutes, it will boot up fine, however the date/time has reset to 1969.  

I have done the obvious things like replacing the clock battery and resetting the pram and smu, but still no joy. I suspect a hardware fault of some kind, but don't know what to try next.