Do a simple charging system test
Ignore the dash light. Borrow a voltmeter from somebody (or buy a cheap one at Radio Shack), set it to the DC scale and touch the probes to the 2 battery terminals with the car running. It's OK if the voltage is low like around 12.2V when idling, but when you rev it the volts should climb to 13.4-14.6V. If it does that then there's nothing wrong with the alternator and you can go back to focusing on the brake issue.
'81 300CD - 180K, cannot be killed by any conventional means
'99 Ford Escort - good MPG