GEN 1 prius P3106 powertrain code and vehicle stalls

Toyota's opinion should probably be represented in the thread too (whether or not anyone thinks it's the last word): the check in the gen 1 repair manual (2001 edition, page DI-8, "BASIC INSPECTION", step 1) is "Is the battery positive voltage 11 V or more", and you "charge or replace battery" if it isn't. I'm pretty sure that's the same threshold as in the later repair manuals.

There are several ECUs in the car that measure their own supply voltages and can give trouble codes if they measure low. The C1241 code from the brake ECU is one example. The thresholds for those codes generally fall in the 8.5 to 9.5 volt range. Remembering, of course, those aren't readings of the battery under no load, but actual voltages seen in operation when a load may be pulling it down.

Certainly it's never a bad idea to check the battery voltage, and in particular if you have any of the voltage-based trouble codes, it becomes an even better idea.

Back when I had a gen 1, it typically started ok down to 9 volts or a little less; it would, of course, log the voltage-related codes, but didn't go 'haywire' or present bogus codes or anything. Below 8 volts I'd more often need to jump it or swap in my spare battery, but again there'd be no weirdness after. I had a fair amount of experience with that, as I usually had some half-baked mod project or other in the works and ran down my 12-volt battery more times than I'd have liked.

 

Is there enough insulation left visible for you to tell what color it was?