Hi Laura
Always go for things that look impossible. You'll feel even better when you pull them off.
When doing something like this, my advice is to have a hunt around, see if you can find some reference to start from. If someone has put their version of the chords on the web, try them out to see if it fits. You may get a few false starts, but you can generally have a good idea of how the song fits together. (Light My Fire is in A and is largely based on John Coltrane's "My Favourite Things" btw).
If there is some particularly complex part that you can't work out by ear, see if there is a midi file of it somewhere, although you will need something like Sibelius to view the file as a score. Making use of the "score" you get out takes a bit of doing as generally you have to do a fair bit of rearranging.
If you're still having problems, in particular if you find that the keyboard player needs a few extra arms, try to find a live recording of the song, or better still, a video (Youtube is your friend). Chances are the studio recording will be overdubbed a few times, and the live version should give you a better idea of the key parts. In the case of The Doors, on stage Ray Manzarek would play the bass parts on a Rhodes keyboard bass with the left hand and everything else with the right. Experiment with different combinations of keyboards and splits until you get it.
Hope that helps!