Welcome to the Powerbook forums!
Do you have any idea what Mac OS version is on the G3?
Many G3 PowerBooks now have dead internal backup batteries that can affect startup. First, try booting while holding the SHIFT key. This avoids any questionable third-party extensions the previous owner may have installed. If you get a normal desktop, then do a regular restart and see if it works.
If that fails, do a "PRAM Zap"" restart and, when you hear the chime, immediately press hold these four keys simultaneously:
command
option
p
r
Keep holding the keys until you hear a total of THREE startup chimes, then let go those keys. Hopefully that will give a normal restart.
If that doesn't work, the following trick is known to help the later Pismo G3s start when the internal battery is dead:
see this illustrated takeapart guide:
http://www.ifixit.com/Guide/PowerBook+G3+Lombard+PRAM+Battery+Replacement/42
Note in Step 4 that the connector between the internal battery is accessible directly below the lower right red circle the artist has added. Without removing the heat shield, gently disconnect that lead from the logic board. Reassemble wit the lead OFF and try a restart.
If that starts the computer then you know its a dead backup battery. This firm still has proper internal batteries:
NewerTech Replacement PRAM/clock battery for all PowerBook G3 Lombard and Firewire/Pismo models
Continue to read the takeapart guide for installation instructions. It's much easier on a Lombard or Pismo than on a Wallstreet!