I had a similar problem and found that a spring that attaches to the handle had broken. I replaced the whole door panel with one from my parts car. The spring didn't look too hard to replace individually.
I'm sure plenty of us have door parts or the whole panel if you need it. Maybe yours just popped off.
Here's a good door pane removal DIY (Also in the 101 Projects book)
Pelican Technical Article: Boxster Door Panel Removal / Boxster Mirror Switch Replacement - 986 / 987