I suspect you solved your problem. Most likely your ALT light would be
on if it wasn't charging right. The previous battery must have not been
able to hold a charge. When they go like this, the alternator's voltage
is supposed to be around 14V when running, but - because the battery
was bad - the voltage was most likely much less than that.

The headlight test is good but a better way is to put a volt meter
across the battery and make sure you see about 14V across it with the
engine running. This would indicate that the alternator is working
properly.

(you can still go to sears, though -- they have a cheap digital
multimeter on sale this weekend for sub $10

Remco