Battery ABS Airbag Light ON Wipers Slowing down

Hi,

I have a 2002 Sunny. Recently, the battery light has been coming ON. When I have my radio and AC on, eventually the ABS and Airbag lights come ON too. The radio almost dies(comes on and off). And my winshield wipers slow down significantly. When I turn all the electrical stuff off, the other lights eventually go OFF but the battery light remaisn ON. I have brought my car to the mechanic and they checked the battery and alternator, which are perfectly fine. They said it could just be a sensor problem. But I doubt it cause my wipers are slowing down!

Anyone got any ideas?

Thanks!