You probably touched the contacts. Apple is too snooty for anything that is human, so the tiny amount of oil that is on your hands at all time(because you are a living human) corroded the battery really fast. Apple doesn't want people touching stuff inside their machines, so they tend to not make the internal parts very durable to the elements. However, for those of us who cannot resist going inside of them, we have to be a lot more careful than with most other things. So you are probably going to have to get a new battery, unless you have some gaseous steel mixed with gaseous hydrocholoric acid in a blast chamber to clean it without damaging it.
If the radio didn't work, you are going to have to dig everywhere the wire is and do an inspection with a multimeter every 6 inches or so along the wire, so you can pinpoint the break. Take all safety precautions of course, it depends on the system you have installed. Once you find where the continuity is broken, take it in smaller intervals until you can see the break in the wire/loop. As for fixing the wire, I'm not the best person to ask, as I will probably give you the wrong instructions given the type of wire. It is PROBABLY just like any other repair, but don't quote me on that.
This may be painful, but it can cost a lot of time and money to replace anything on this bad boy. I've owned this exact laptop. I replaced the motherboard twice, 3 new hard drives, a new keyboard, and a new screen. I'm not gonna say how much it cost, but it's not worth it with this thing. It lasted 3 years for me, and by that point the CPU was almost ready to die on me. If you wan't to put the time, money, and effort into replacing this thing, pop the little border off the edge of the screen and find out what kind of ribbon it is that you have in there. Then you can put a replacement in while making sure to use anti-static everything in the process of it.