Thanks for all the suggestions / comments - particularly Rob (Bert320) who has provided me, on spec, an ECU for Williams to try.
My old ECU is definitely dead but there is no indication that there is a generic problem with the MBE ECU hardware from that era, which was a key part of me creating my original post. The problem is now with finding the right map for this 140bhp, Piper cam'd engine (not 150bhp as is referred to in some posts above).
The current situation is that we have 2 MBE ECUs which seem to be sound (Rob's and a used one provided by Caterham), but Caterham are apparently incapable of finding the right map to put on them. The one they can provide will not run my car at all and another map copied by Williams off a similar car will run mine - but badly. If they are providing the "right" map then maybe the car they sold me actually does not have the engine in it that they said they were selling me......!
The current plan seems to be for Lee from Caterham to visit Williams and "sort it out". My preference (and Williams') is to get Caterham to get my car running, but I appreciate that I may have to resort to getting a map specially made if this proves futile. But why I should have to pay to go down that route for a standard spec car bought direct from Caterham would be beyond me.