Top stuck closed
 

2001 Base Boxster. Top is stuck in closed position. Clamshell will NOT move. At all.

I press the button and get a sound that something is trying (1 muffled click/clunk, then nothing). Clamshell will not budge.

How do you get the clamshell up so you can access the cables? There's no access otherwise.

Reach from the inside and pop the ball joints on the lifting arms off if you can. I couldn't and unbolted the arms from the transmissions:
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Note: I fixed the car later by replacing the microswitches in the top latch.
Troubleshooting procedure here: https://www.justanswer.com/porsche/3vq2d-own-2004-boxster-s-the-top-will-not-go-down-when.html

If you have the original toolkit there is a tool for popping off the ball joints ans instructions in the owner's manual...

I'll give that a shot. But, lets just say I wear extra-large gloves. I don't have small hands. It's extremely difficult for me to get in there and work with the top up and the clamshell closed.