actually if you use twisted pair leads it does help for noise rejection. the car is a noisey car unfortunately and what may work for one may not work on another.
you can do that if you wish. cheap way out (if it works fine.) is to get a band expander ($29) and chuck that inline with the antena so the radio works.
if its died - swap the radio with a local one- I had a customer today that did this with a pioneer unit. jap unit died had a 12cd behind it. so we put a local 5850 in it's place.
you have a loose rod in the drivers door. if you can hear the actuator going in the drivers side then everything else is fine. tear the panel off and screw the rod back in place.