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See if you can boot from the Leopard CD by holding the "C" key at startup. If it starts, then the logic board is probably OK. I suspect the LB will turn out to be OK.
When I get an older Mac that's likely been off wall power for several months, I start to suspect the PRAM battery which has been mentioned earlier in the thread. Depending on model, a dead PRAM battery can mimic a total logic board meltdown, demonic possession, or only create a minor glitch.
The G4 uses a 3.6V 1/2AA lithium battery. Radio Shack has it as part number 23-026 but it's overpriced IMHO. I buy them online for about US$5 and stash the supply in the veggie drawer of the frig to keep them fresh a little longer.
I order batteries from
this vendor and pay shipping, or from
this vendor who pays the shipping even on small orders.
Bt all means, if you need the battery right away, there is no denying that Radio Shack is the best option if you can deal with the $15 price tag.