Reboot the key processor:
Remove the battery
Wait 10 seconds
Put the battery in backwards (yes, this is a procedure recommended by Porsche)
Wait 3 seconds
Remove the battery
Put the battery in correctly
If that doesn't work, check the contacts that connect the button switch to the circuit board. Years of mashing the button often breaks these contacts so that they make intermittent contact. With intermittent contact, often the light will flash but the discontinuity causes an irregular signal to be sent and the car doesn't respond.