alright, first of all if you like the car, you can't let some little problems have you on the verge of selling it. If it's your only car, I can see how it could be a problem, but if it's a "back-up" or "fun" car, just have some patience and take a break from it.
That being said, for the stereo and locks, I'd check the fuses first. Fuse 11 for the radio; fuse 8 for the gas filler door; not sure about the locks. I'd just check all of them to make sure they're all good.
Buy yourself a digital voltmeter ($30 or so at autozone) and ohm (check resistance) the battery cables. If you have very much resistance (mine are always 0, so I'd say much more than that and I'd replace them for sure). If they're that bad, just go get some new battery cables and put new ones on there. They're like $15 or less at autozone and that's if you get the 4ga cables. If you're going to replace the cables, the voltmeter wouldn't be necessary, but definately nice to have. I use mine ALL THE TIME.
About the starting and dying thing, it very well could be your battery/battery cables. Does your check engine light come on? Does it just all of the sudden die or does it hesitate or surge up and down and then die? It could be a lot of things, but I'd replace those battery cables first.
Good luck and post back with questions/results