No the Pismo works fine with the PRAM battery disconnected, obviously with no time saved/other PRAM settings. I've found that plugging the PRAM connector back in while the machine is powered up can "jumpstart" it again and it'll charge up, so you can use it normally without having to unplug.
I recently fixed a PB Ti 667Mhz which had the 3 - 4 flashing LED/beeps at startup, by cleaning the RAM contacts with electronic cleaning solvent spray. It only ever used to start up 1 out of 20 times before this repair. So I'd suggest going over the CPU daughtercard contacts, and motherboard with similar stuff, and checking for any damage. If you push down hard on the CPU, does it boot then? That's been my way of diagnosing many a dodgy PC/Mac laptop - the old "press or bend here firmly" can bring many flaky machines back to life, for a moment.
JB