2001 Boxster S Battery or Electrical System Problem?

Sounds like a dead battery to me. Not too surprising at that age, especially if it has been run right down a couple of times. I would go to your nearest battery specialist and get it checked. Then, if that is the problem, get the best quality compatible battery they do.

In the older 911's (80's) there was a grounding strap from the engine to the chassis that would cause this sort of problem from time to time. Check for such a strap, clean terminals and starter terminal.

On my '69 912 I had such a problem and it turned out to be the 1/4" x 2"(?) copper bus bar inside the solenoid--arcing had badly pitted the contactors. It _supposed_ to short out the terminals from the battery to the starter motor. It was a little more intermittent than you describe. I simply replaced the solenoid and never had any more problems.

Do you hear a _click_ when you switch to the _start_ key position?

Thanks for your input!