2000 cougar won't start

After inserting the key and turning it to the run position, all dashboard lights go on as usual, headlights and radio work properly. When I turn and hold the key to the start position, the outside temperature display, the radio, and the door open indicator light go out. Only noise heard at this time is small relay click from relay #2 and the car does not start. Headlamps and interior lamps remain at the same brightness.

When the key is allowed to return to the run position, the outside temperature display, radio and door open indicator light go back on.

Starter, PCM computermodule and starter-relay repaced.
Rotating all the relays by one position does not help.

Hopefully you can.