It sounds like the car is acting as if it thinks the key is in the run position and has not been turned to the start position. The oil measurement only happens if you turn the key to run and leave it there without starting the engine. Waiting to let the computer check the oil level is not mandatory and should not effect your ability to engage the starter. Your Boxster should start just like any other car.
I think if you search on this forum you will find a lot of posts about faulty ignition switches. I'm betting that is your problem. They usually start out intermittent and then get worse.
See this recent thread for more information for example:
http://986forum.com/forums/general-discussions/46998-need-key-ignition-help.html