While the charging cable is connected, gently lift UP on its connector jack and see lights come on or you get some other indication of charging. These internal connectors take a lot of abuse over time; lifting the connector slightly restores contact temporarily with the power board.
And I'm pretty sure your PRAM battery is bricked too--that can prevent starting. If you decide the power adapter is getting power to the computer, remove the keyboard and locate the PRAM battery cable. It can be seen as the red, white and black cable in the "Step 3" image on this site;
It connects to the logic board immediately to the left of the right-hand heat shield retaining screw. Disconnect it. With most Pizmos, disconnecting a dead PRAM battery will let them start.
If the comptuer then starts, you need a new PRAM battery. I've bough several G3 powerBook Pram batteries from OWC and they have worked fine. This is their offering for the Pismo:
I heard some sort of clicking as if the HD was trying to boot but was not being allowed. So I tried the jiggle power input but no reaction. The PRAM Cable removal did the trick, instant on. I will be ordering another PRAM battery as you suggested.
I remembered this solution from some long ago issues but failed to initiate on my own this time.