Starting problem

Ok, so I picked this car up for $500, and have already put over that into it with lights, 16" Pony wheels, and tires....so I' m not expecting too much. Although I' ve gotten my headlights installed (give or take some adjustment, and modification to the header panel), fuel guage miraculously started working, fixed the windshield washer, re-attached the rear view mirror, and fixed the dome and map lights, all since last Saturday. One problem I' m experiencing, and the source of the problem eludes me, is a starting problem. The car can sit for a month, and start on the first crank every time. If I drive a few miles, get the engine warmed up, and shut the car off, 9 times out of 10....it won' t re-start without a jump or booster pack. If I allow it to sit for a little while and cool off, it' ll start fine, no slow or hard starting. While it' s running, the battery guage will read one mark below center, but when I shut it off, it' s a little above the red zone. Does any know what would cause this? Both Pos and Neg cables have been changed, they were corroded as hell.

Thanks for the tips man!