2000 Nissan Maxima Alternator/Starter

I bought this car used 4 months ago and love it. Had trouble getting it started the other day, but eventually it did. Once I got it started various lights started blinking on and off on the dash (seatbelt, battery brake light). Drove it to get a new battery (first suspect) because it still had the original in it and it died on the way driving there. Once I go the battery in, it is now starting just fine, but the light problem persists. I haven't driven it too much though. Any chance it is the alternator. The only other thing to add is a strange whirring noise (sounds like ball bearings maybe in the alternator) which persist for about 10 seconds on startup which it has been doing since I bought it. The dealer said he had three other used maxima's on the lot which do this and it was not an issue, just a common noise they make. Perhaps I should have believed him, but I got a good deal on it understanding I might have to fix something like this.