There's no connection between the gearbox in limp mode and the fuel pump. If its been stood for a while then its entirely feasible both have failed at the same time, being two of the most problematic bits of the car.

The only way the F125 can cause a no-start condition is if it fails to engage the neutral relay when in P or N - that is a relatively common problem as the contacts in the switch burn out or simply fall off. The starter doesn't engage at all then though - you turn the key and nothing happens. That doesn't put it in limp mode though because the TCU doesn't care about that circuit. If its turning over and not starting then the neutral switch is ok. Instant PRNDS when you turn it on is mostly a sign of 'F125 implausible', but also can be symptomatic of a wet TCU getting solenoid and valve body issues on power-up.

Is the rev counter moving when you try to start it?

As MJ says, the F125 can also stop the car starting, as happened to me, but it's separate circuits inside the unit (re starter relay) and it won't turn over, so not the problem here.

Hi! Glad to hear you still have the car.
It seems around the 20 year mark is around the limit for these old fuel pumps. I guess 20 years work is very good for a brushed motor fuel pump.
I still haven't got round to starting on mine, been abroad for a few weeks.
I have the new pump already, but now I have to hunt around for all the seals and washers etc before I can start the job. And I'll have to buy some cheap run around car until this is fixed. What a pain.

I hope you get yours sorted. These are such nice cars, there is nothing new that can replace them.

*edit - wrong thread