The door lock won't be the issue. The fact that the key will lock/unlock, the doors lock and unlock, and (I assume) the windows drop when the door is opened, means that the motors and microswitches inside the lock are all working. (Again on the assumption you are not getting a double-beep when locking). Even if there was a problem inside one of the locks, it wouldn't have any effect on remote locking.
It sounds like the key radio remote signal isn't being recognised by the alarm unit. The 'input signals' check with the Porsche tester should confirm that. That's the first thing you would test if the remote doesn't work.
I personally think that there was some occurance that caused the fuse to blow, and in doing so it has caused the alarm module to lose the radio remote settings. A new key would confirm that, but I appreciate it is an expensive option.
If you can lock the car with the key, without getting a double-beep, and there are no fault codes shown in the alarm module, it would appear that everything is working as it should, albeit the key button isn't. Should you go for a new key (and it works) ask to keep the bar code label, so that it can be re-programmed if it happens again.