The key head is never programmed. Each key has a unique code that it sends and the car is programmed to recognize that code. You could program multiple Boxsters to recognize the same key code if you wanted. There is a possibility that the car has "forgotten" the key that doesn't work but I wouldn't consider that first. Besides, in order to reprogram the car you need the code that comes with the key, which most people don't have (it doesn't come withe the original keys).
Here are some things to try:
1) Reset the key head: take the battery out, put it in the key head backwards for 10 seconds, then taking it out and putting it in correctly.
2) (You cited this incorrectly so worth retrying) Reset the receiver: switch on the ignition, switch off the ignition, remove key, operate transmitter within 6 seconds
#2 is needed if you try more than 256 times unsuccessfully to unlock the car. Once you get to 1024 this won't work anymore.
The other possibility, which is common with the early key designs, is that the contact between the remote button and the circuit board is intermittent. When you press the button the light may come on but any even slight interruption will cause the transmission code to get garbled. The solution to this is to reflow the solder connections with a fine-tip soldering iron or low-temp reflow gun.