When you say that you have removed the door handle, do you mean the inner or outer one?
The outer one is easily removed too, mine actually fell off (whilst my wife was driving funnily enough).
As I remember it, there's a small plastic/rubber grommet on the side of the door by the door latch/locky thing, that pops out giving you access to the thin metal sliding bit that holds the outer door handle on.
If it was my car, that's what I'd take off first to check, it may give you more of an idea of what's not working properly. The door opener is mechanical rather than electrical so it may be something obvious.
BTW my Bimmer is a '98 528i so probably exactly the same.
Good luck and let us know how you get on.