Problem with Parking Lights

I just installed a new Kenwood headunit in my 4dr Blazer 1995.  Anyway I tested it before I put every thing in and it worked.  After a while my battery died(I left my dome light on while I was doing stuff but Im not sure if I killed it or not).  Anyway I jumped it and some strange things happened.  At first my Speedometer was going nuts.  I had the car in park and it went up all the way to 100 MPH.  After a while it went down to 0 but I am still having problems.  My parking lights for one dont work at all.  I checked the fuse and all that but nothing.  My car also dies after I turn it off, even if I try to start it 5 seconds later, it wont even come close to starting.  The gauges on the dash work but I cannot see anything else.  I used a wire harness to do everything.  If some of those wires touched while I was testing it could it have messed something up?  Before I even installed the headunit my car has had lots of battery problems that come and go.  My battery would die a lot until I hit a bump and it didnt seem to get problems anymore(I guess a conenction wasnt on tight).  I read posts earlier that said the problem was the BCM.  I was wondering if that would also cause the car to not start properly.   It was going to go to a mechanic regardless because of the problems but any info on what might be wrong with it would help greatly. 

Change your battery. If you can get a friend to borrow his/her battery ( a good one ) from their car and try it on yours truck and see if the problems persist. This way, it's an inexpensive way to test if you need a new battery or not. If the problems are still there, then I would look at your alternator next. If the charging system is not your problem, I would look under the hood at the fuses under the hood by the battery for any burned out fuses. ( Use a DMM and not a light tester on these because the DMM is more accurate in detecting broken fuses ). Make sure you have the ignition turned ON when you test the fuses. They should all have current going through them. Post your results.