Problem starting the MK2

The new car 98 Roadster RS.

Got a weird problem with the MK2. Thursday it wouldn’t start, turns over, but the fuel pump doesn’t seem to be running, the relay seems to be clicking . So I pulled the carpet up and there only seemed to 5v at the F/P connector, so I jumped it from the Volvo fires up instantly. yesterday exactly the same thing turns over, but won’t start, again jumped it and it works instantly.Swapped the battery from the MK1 yesterday, this morning same thing, refitted original battery that had been on charge over night and it starts on the button. Check wriggled, cleaned every thing I could find under the bonnet.  Now have to wait and see what happens in the morning.

Any ideas why the fuel pump won’t run if the voltage has dropped, but still enough to turn the engine over?

 Once it’s started it’s fine for the rest of the day. I really don’t think it’s battery related it spend 5 days under snow last week and started 1st time.

 G’day Miles
Sounds like bad connections at the battery. Changing the battery over seems to have disturbed something

Suspect it’s a bit more complex than that. Started OK just now, but it was a good 5 degrees warmer last night than it has been (battery showed 12.65v before I started).