Possible short causing batt drain?

Hi. First offs.... 98 Sonoma Extended 3rd 2.2 step. Ok, I just bought this Saturday, and well, am a little nervous. When I go to start it cold (been sitting overnight or like 8 hours at school or something) and I turn the key it's as if the battery is almost dead. Just err, pause, errr, pause, start. But if I drive to the store or somewhere and it sits for like 30 min or so and I go to start it up it's fine. This leads me to this...at the dealer's the wire to the mirror [for the lights] was unplugged from the mirror. I can see a bit of electrical tape up at the top, leading me to them doing work on it. When I changing tail light bulbs, I can see more electrical tape on the wires, leading me to more electrical work. Under the hood I can see MORE electrical tape. Is there a way to test if there is anything using the battery? It's like the cables are corroded, but they look brand new, although they detailed it so they could be corroded on the inside. What should I test first?

first check your battery to se if you have a dead cell if you have a dead cell the battery will hold a charge during the day but will dream down over night