Intermitent Brake Warning Light Problem

I own a 2001 Toyota Camry with aprox. 75,000 miles. For aprox. 1 mos. Now my brake light will periodically go on (especially in the morning when the engine is cold), it may stay on for 15 seconds to a minute, go off, then possibly come back on in a short while. On occasion (albeit rarely) my clock has gone blank and my driver side automatic window has gone down and up very very slowly, only to both work fine the next time I start up the car. I recently replaced the battery, but that did not seem to make a difference with the brake warning light comming on then going off. Would this likely be the alternator which is going. & If not, what would be the possible cause, given these symptoms. Thanks in advance for your assistance.
Pete