ford ranger electrical system malfunction

hey all this is kind of a weird problem im having.  i have a 96 ford ranger extended cab 4 cylinder.  i left my door cracked open one day and the chime drained the battery.  the battery must have been pretty weak but i did leave the door cracked for about 12 to 14 hours.  i was able to get the battery jumped off and didnt have another problem until one day i went to start the truck and it was dead.  i had a friend come out to help me jump off my truck and when we hooked up the cables to the batteries the battery in my truck started to make loud popping sounds and a wire on the right side of the cab started to smoke really badly like it was about to start an electrical fire.  this all happened in a span of about 5 to 10 seconds as long as it took me to get the cables disconnected.  i called my friend who is a mechanic and he said that it was either that i had the connections backwards or that the battery was about to explode.  my friend said that he looked at the connections when i made them and they were right so it was kind of scary that the battery could have exploded in my face.  when i went to take the battery out of the truck the ground cable on the battery was in pretty bad shape.  the terminal was so corroded that it basically disintegrated when i tried to get the terminal disconnected.  i had to cut the cables and put new terminals onto the new battery and the truck has run ok ever since.  the problem that i have is that the radio has never worked since then.  i thought that the radio had a fuse on the back of it and that it was blown so i never thought much of it i just never pulled the radio to see.  i found a clarion drx8575z cd player from my old car and decided to install it into my truck.  i bought the appropriate dash install kit and wiring harness and soldered the wires together.  i made sure that all the proper wires are soldered together according to the instructions included with the wiring harness and the wiring schematic from clarion.  i went to put the stereo in my truck and i have nothing.  i have checked all the fuses in the box on both the side of the dash and the box under the hood.  i dont know if there was some wiring damage from when the battery almost exploded.  there is some charred wiring on the right side of the dash right next to what im told is the fusible link.  i have uploaded some pics to try to show what was damaged and where everything is located.  sorry to be so wordy but i wanted to be as descriptive as possible.  any help would be GREATLY appreciated. 

right side of the engine bay.

i tried to zoom in to show the charred wire but its really blurry.  if you can take anything from it then let me know.

You need to get a volt meter and verify you have your red, yellow, and black wires hooked up correctly.  If there isn't voltage between the black and red wires and the black and yellow wires then the radio isn't going to work.

Once you discover what you are missing you can figure out why you don't have it.

ok i hooked everything up and checked for power at the point where the harness for the cd player and the factory harness connect.  i have nothing.  fuses are good and i cant see where the wiring goes so i am having a hard time tracking down where the wiring goes into the firewall.  it gets even worse under the hood.

Yes, you will most likely need to hook both of them up (to seperate sources for it to work right). 

It sounds like you may be in over your head - I would sugguest taking it to a shop where they can install the radio correctly and safely - without the risk of damaging the truck more then it already is!