hmm i'm not sure how they are wired, i doubt they will use crossovers which is the norm with components, so it could well be the tweeter is piggy backed from the door speaker and if so then it definitely isnt a head unit problem, it could be a lose connection either on the tweeter or to where the tweeter connects (the speaker)
not that it matters really, if you buy components you will tkae the siganl from the left speaker (which is working) and use a crossover to the tweeter
or as in the link above you could fit a speaker that has bass,mid and tweeter built in