1996 Mondeo Starting problems.

Hi all.
My wife has an old Mondeo. It's one of the first Mk2's, built in belgium in nov 1996 and registered in feb'97. It's a 2.0 litre Ghia
hatchback, manual box.
The problem is that it will start OK from cold but won't restart once the ignition circuit has been active for about fifteen minutes. A better explanation is needed.
Start from cold, runs fine. Drive around normally.
If we leave the ignition on for some reason (such as driving the car! But I've tested it by turning the ignition on from cold and leaving it, engine not running, and it still happens.). Stop for a level crossing / stall it / nip into a shop or something THEN try to restart the car. All we get is the engine turning over without any attempt to fire for about five seconds. Then the starter motor stops, the wipers flick across a couple of times and thats it. This is the wierdest part of the problem. At first I thought I was knocking the wiper switch but no, it's the car wiring at fault. We have to leave it for three to four minutes for... something to cool down?... then it will restart normally.
The battery is a new (now 8 months old) heavy duty one. It is always fully charged, it always starts well from cold on even the most frosty of mornings. (We've had this fault for over a year now.)
My (non) diagnosis:
The starter turns at full speed, not slowing down, not chattering. Therefore the motor itself seems OK.
The motor turns, so the the wiring to the solenoid must be in place.
The engine makes *no* attempt to fire, therefore the ignition circuit must be compromised somehow. Or is it the ECU?
The flicking wipers make me think that a current is finding the shortest route back to earth. Which means maybe an important earth for the starting / ecu system is broke?
Can anyone point me to a possible cause? Are there any common faults that could manifest themselves like this?
Thanks for any help.
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