Mac Pro G5 Fails to start

i have a Mac Pro 5G (yes it is old - no intel chips). today i went to start it up and it failed to start. it is plugged into a Balkin battery back up.

When i pressed the power button, i got the gray start up screen with apple Icon and spinning curser. it just stayed spinning and the fans ran faster and faster until they were screaming at me. i had to hold the power button to force it to shut down.

when i tried to start it again, it started the boot, chimmed once then did nothing...no gray screen, logo or nothing. i repeated the process severa times without change.

i disconnected all the peripherals, with no change.

i then pulled 2 of the 4 RAM chips. tried booting and again it hung, swapped the chips and tried again...she started up. thinking i had a bad RAM chip, i tried to put them back in (one at a time). it froze up again......still thinking it was a ram chip, i dropped down to the two that worked, and it hung again.

i did get it running at one point, logged in it would suddenly go to sleep, i would enter a password to unlock the screen saver and it would then go back to sleep. finally it would not wake back up.

So i am at a loss. things that come to mind: Logic board, hard drive or power supply. unless there is an under volt, i don't think it is the power supply.

any other thoughts?