Auto Parts: 2005 Hyundai Sonata - Dead Battery, 2005 hyundai sonata, windshield wiper blades

Question
I bought a 2005 Hyundai Sonata in May, 2009.  Up until now it has been a dream.  I accidently left the dome light on this past Friday night and naturally the battery died.  Well when I tried to jump it on Sunday afternoon, it would not jump.  I know I hooked the cables up right, red to red, black to black.  When there was power flowing the trunk latch kept working as if opening and reopening itself, and the parking lights came on, without the keys being in the ignition.  When I went to try to turn the car on to see if it was working the windshield wiper blades would turn on.  Now I had pulled the clock fuse under the dash and it wasn't blown so I just put it back, and then my dad checked it was.  Not sure if that had anything to do with it or not.  We put in a new Delco battery Monday night, but the battery light is still on and my mechanical technicians are going to look at it today, but I was wondering if there was anything like a computer reset I need to have done or anything like that.  The intermittent function on the wiper blades does not work, nor do they turn on when I spray the washer fluid.  They only work in on or the faster setting.  The heater/air cond. fan does not work either.  I can hear the blend doors moving when changing from vent to vent, but nothing is being blown out.  As far as I know everything else still works.  I have read that Hyundai batteries are not good, and I know the battery that was in the car was not original.  There are almost 118,000 miles on the car.  Please help.

Answer
    First of all, you can't go by the color of the cables.  You have to actually look at the battery and identify which is positive and which is negative (there are little + and - signs molded into the battery case).  You must do the same for both the jumper and the jumpee.  Make sure that you hook positive to positive and negative to negative.  But that time is passed for you.  Are you sure that you put in the correct battery?  Batteries have what are called "group numbers" which are displayed on the label as part of the part number.  Buying a replacement battery at a Pep Boys or some such den of iniquity can frequently result in a battery that fits in the car physically but is not otherwise correct.  Part of the group number is the polarity specified for the particular group.  You may have the wrong polarity installed in the car now.  You want to find the cable that goes to the starter motor and make sure that it is connected to the terminal which is labelled "+" on the case of the battery.  If it isn't, then that is your problem.  The starter cable is always connected to the "+" terminal on cars built after the '50's.  If you made an error when jumping the car you may have burned out a fuse link.  There are several of these attached to the terminal of the positive cable and they are used to isolate certain parts of the car's circuitry from the main bus (fusebox).  They are easy to damage and easy to replace.  It is possible, if the jump start was performed improperly, that the ECM which controls the engine has been damaged.  A good mechanic should be able to figure all of this out for you.  It may turn out to be an expensive problem.  I have a feeling that the battery in there now is the wrong polarity since the items which you mention not working are DC motors which will only turn in one direction.  Wrong polarity would mean that they won't turn at all.