HP-71b does not turn on when using batteries

[cruff]

If there were a short or other cause of excessive current draw in the unit, I would expect that when powered by the AC adapter for it to behave similarly, as the AC adapter, through the bridge rectifier and regulator transistor, is unlikely to be able to provide more current than the batteries can through their blocking diode. The only difference is that the rectified AC voltage before regulation would be higher, which might be enough head room to allow it to run.

The service manual has some power supply diagnostics, do you have a DMM to perform some basic measurements? When active the unit should only draw about 10 mA, with no modules plugged in. If you have anything else plugged in (RAM, ROM, card reader, etc.), remove it and see if it behaves or not.