electrical help please!

[glendale]

hey guys i am on the 60-66 side most of the time. i have 03 tahoe also though. tonight i went to dinner with the wife and then to walmart. we came out and the tahoe would not start and the lights were super dim.oh and it smeeled like rotton eggs under the hood. so i went back in an bought a new battery. we have had the truck for 3 years and never replaced it. so i said why not. well now with the new battery the lights wont even come on. so i put a volt meter on it 12.53 volts then i checked the old battery 12.43 volts. about that time the lights kick on. and the new battery smells like rotton eggs. and it still wont start. the positive lead is HOT to the touch. i also tested voltage at the red box that comes off the alternator and it was 12.43. so what do i do now? any tips will be greatly appreciated. i work on old cars without all of the mumbo jumbo.