Toyota Repair: 89 corolla, alternator output, battery terminals

Question
Battery light and brake light on dash came on, after driving for 3-4 days car died. I replaced the alternator (was tested as bad), the 2 dashlights are still lit. The voltage reading at the battery when running is approx 13.3-13.6V. this stays the same when all accessories (loads) are turned on. According to the manual the voltage should be 13.9-15V. Also when the parking brake is released the brake light stays on but is slightly dimmer.  

Answer
I think you still have a problem with the alternator, or maybe the battery has an internal failure that won't let it charge, I suggest you have the alternator output tested under load, not just voltage but amperage as well and load test the battery. The voltage reading you get at the battery terminals with the engine running depend for the most part on the battery's state of charge. 13.5 volts is normally enough to keep the battery charged up.