87 4000S fan runs...and runs...and runs...

[Robert Phillips <R3RFP@VM1.CC.UAKRON.EDU>]

Greetings fellow Audi lovers/haters,
    I have a 87 4000S, 4-cyl 1.8L and it is misbehaving in typical Audi
 fashion.  Electrical problems.  The radiator cooling fan will not stop
 running unless I switch off the key.  It runs regardless of engine temp all
 the time.  I thought: switch in the rad., or stuck relay.  I replaced the
 (two pin) relay with one from a friend's Fox (three pin).  It still wouldn't
 stop.  I swapped the relay with one from another part of the fuse panel, and
 it still runs.  I am in Ohio and don't need the fan running constantly.
   Any ideas guys?
                         ---Bob