not work after I jumped the car After jump starting my BMW Z3, the power windows, central locking will not work. Is this something I can fix myself?

These guys are morons or something. That is either a blown fuse or a tripped breaker. Check your fuse panel box, on the cover it will say what each one is for. find the one that says power windows and pull it out and check it, if it's a fuse. If it's a little silver box about 1-1/4 in long, it's a breaker, and has tripped. Take it out and then put it back in,, that should clear it.

This happens from time to time, I believe it's due to a glitch in mechanism, I've had that happen on my 525 and also opening trunk internally, I'd take it to dealer get it checked as soon as your next inspection is due or oil change, I had to bear with it for some time, as I didn't have time to take it in. Problem goes away by itself, it can be at any given time. (Obviously consult your manual) Most likely it'll say to have it checked, (No time) As I said it should go away at any given moment.

I didn't fully read your question, very strange you jump started it, you are not supposed to, you would throw off the mechanism, you should've called road assistance, (should be part of the package, for a new car) otherwise could end up voiding the warranty. You might have a problem, you need to call or check for the problem at
http://www.bmwusa.com/

By the way, if this is the case, you really don't have a choice but to take it to the dealer or a BMW specialist. I know of one, where are you located?
Hope this helped.