Mr. Elbe said:
The battery light being on indicates no charging. Most likely the
battery reversal not only blew fuses bat also a fusible link. Worst
case, it fried the diodes in the Alternator.
Actually, there's an even worse case..... in most newer vehicles, the field
on the alternator is controlled by the PCM (ECM, Computer, etc.) This means
that there's the distinct possibilty that you'll need to change that to fix
the problem. Find out what the field pin is on the alternator, and see if
it's at 12 volts (or so). Then look at the the output lug of the alternator.
If the field pin is high, and the output is not at least (at the very
least - it should be closer to 14) 13 volts, then the alternator is sick. If
there's little to no (less than 6 volts) on the field pin, then the computer
is sick.