Finish incomplete degree before returning to school?
Off the top of my head, I can't think of anything that would stopping you from starting over fresh in this case - you can retake every course, restart your thesis, etc. if you so desire. (That being said - I'm not an administrator.)

That being said, it's also probably worth your time to get a copy of your old transcript (if possible) and talk to any prospective universities about transferring old credits. It may or may not be possible for every course, but I'd be surprised if absolutely zero of them transferred.

The advantages to this approach are numerous, to say the least: 


It's most likely cheaper.
You'll almost certainly complete your degree faster.
You can skip ahead to the parts of the program that most interest you without having to worry about prereqs.


As always, however, you'll have to check with your institution of interest as to what their specific rules/procedures are. Beyond that, I imagine it's hard to say with any certainty what to expect.

That goes for returning to your old university too -- they'll know best what your first steps will be.