Stala
Welcome to the Discussions.
How long was it since the PB was last used? Had the batteries (it sounds as if you had two of them) remained in the PB since last use? Was the AC adapter attached and powered-on the while? If not, have you left the adapter attached and powered on since attempting to start up?
Problems arise when the internal backup battery depletes during storage. The PB then has no way of knowing what startup device to use, where that is and (very probably) which day of the week it is because the settings in PRAM have evaporated or been scrambled. If your batteries are originals, their internal EEPROMs (which are supposed to keep the batteries 'smart') will also have lost their settings. Take the batteries out and disconnect the AC adapter if that has been atached. Let the PB stand for 20min or so.
Then press, and hold for 20sec or so, the keys control-option-command-power (the left-pointing triangle). This is to reset the Power Manager. The PB 500 series has no dedicated reset or interrupt switches. Reconnect the AC adapter, wait five minutes, and then attempt to start up. Repeat, if this is unsuccessful, a couple of times. If you still get no joy, leave the AC adapter attached for a couple of days, with the main batteries inserted, and then try again.
This article and
the repair manual may be of use to you, but your starting point has also the disadvantage that the batteries are already out of the race. That is, you may have to do some coaxing of the main batteries to be able to get the backup battery also to take some charge. (Only if the AC adapter does not become warm to the touch during attempted recharge of the main batteries need you suspect the adapter of malfunction.)
Do you have install floppy disks, and the Disk Tools, for the PB?
Apple IIe; 68K: 11DT + 4PB; PPC: 5DT + 3PB; G3: 6DT System 6.0.8 to OS 10.4.x