did you spill beer on the charger, particularly the where the Magsafe plugs into the Mac? If so you may have fried the charger. I have seen on here cases where the charger will power the Mac, or charge the battery, but not both. You may have one of these. If that's the case you are lucky, you need a new (cheap) charger not a $$$$ new logic board.
If the Mac boots OK with the battery in, we have a number of possibilities
- if everything is OK, you may have a firmware problem, "Free" to fix
- if the Mac won't charge the battery, you could have a fried battery, charger, DC in board, or logic board
- etc etc
we really won't know until you have got the battery & charger plugged in and you know whether it will boot or not & then if it boots whether it charges. As iBookG4user says, it's hard to diagnose until the Mac is in its default configuration.