2005 Hyundai Elantra Electrical problems after battery was

My sister has a 2005 Hyundai Elantra. Her battery went dead after leaving the dome light on all night. A neighbor gave her a jump in the morning so she could get to work, but he hooked up the cables backwards. She told me that it sparked pretty good. He eventually did get the cables hooked up properly and the car runs fine. That day the aftermarket cd player stopped working. I checked the fuses in the car and changed them out for new ones. Cd player still doesn't work. So, I pulled the cd player out checked its fuse and changed it, still nothing. So, I checked the power wires for the cd player, there is no juice coming in to the cd player from the cars radio wiring. The wires are dead. About a week later the dome light quit working and so did the map lights. Now the dome and map lights will flash on and off on occasion without touching them. She also stated that when she puts the key into the ignition to start the car that the rpm and speed needles go up to top speed and top rpm and then drop to half way. The factory car alarm and keyless entry doesn't work anymore either. She told me that right after the neighbor jumped the car and she got into the car to go to work, she smelled a strong metallic burining smell. I know jumping a car backwards can cause electrical problems. She thinks it is just the cd player. I keep telling her that she might have damaged the computer in the car and more electrical problems are going to happen. What do you think happened from the backwards battery jump? How much damage can be done from this? How much future damage can I expect? I would appreciate any information you can give me on this matter.

Thanks,

Kevin Morelock