<<The rubber boot should just be able to pushed off. The broken wire probably does >NOT< have broken insulation, so you won't be able to tell its broken just by looking at it. You'll have to do a continuity check.>>

I just wanted to add one thing to Kim's comment.  It is sometimes possible to get a good continuity check, and still have a bad wire. How's that you say?  The wire may be capable of carrying a very small amount of current, but not enough to power the actual device.  I think I must have spent 8 hours trying to get power mirrors to work, and finally ended up replacing a wiring harness that checked good.  Drove me freaking crazy!  I would say to use a tester that has a light, and not just a simple continuity tester. It's not good enough in many cases!!.  The area between the door and dash is very common for wires to break or become brittle, just because they are moving all the time there.  I certainly think it's a good place to start.

There are lots of good sources for connectors if you find you need to make up a new harness.  All I can say is take your time, be methodical in testing, and the problem will usually reveal itself.  It certainly can be frustrating, but it's also a great feeling when you get things to finally work.

Troy