Could be your alternator? That's what keeps your battery charged up while the car is running. Corrosion could cause a bad contact in your fuse box, that could be why there are some things not working...Loose wires by the wiper motor sounds like someone somewhere along the lines had a problem with that better find out why there cut, maybe a direct short if one of those wires comes in contact with some metal...Look under the dash and see if any wires were cut under there...Sounds like you better have someone take a look that knows electrical stuff...I had a wiring harness wear through and it started on fire...Not a good thing....Hope this helps ya...I'm sure the guys will give you some ideas too.... 