Does the calculator respond to pressing ON and / simultaneously? If so, you could try an INIT: 1 (by simply pressing <ENDLINE>) which is the approximate equivalent of a machine reset (ON + C) on the Pioneers, i.e. it just gets you out of any infinite loops and into a defined state (with USER mode off so all standard functions are available again. It will not destroy any data except maybe, if I remember correctly, the command stack.
Next thing you could try is INIT:2 (ON /, then 2, then <ENDLINE>) which does a ROM check. By the speed of it, I'd think it is merely a checksum test, but it'll still tell if any of the ROMs are faulty.
If the test passes and your machine still won't run, you could have a problem with the RAM or the main PCB. I have no knowledge about the 71s internals but from the amount of RAM initially installed (17.5K) I'd guess that 16K are in one chip and the lower 1.5K are in another. The OS uses the lower addresses first, especialy for its internal purposes, so that's where I'd look for a problem. You could have a hairy crack in a trace on the PCB, for example, which, if you find it, would be repairable.
Keep us posted about any results.
Cheers, Victor