Could be a fuel pump ECU problem. To bypass it, use a paperclip in the diagnostics port under the bonnet (next to the oil dipstick). Join FP and B+ to force the fuel pump into "ON" mode, bypassing the ECU. Turn the car to ON and you should hear the pump working (hopefully). Try starting the car and going for a drive similar to when the problem first occurred and see if it still happens.
If the problem goes away, I'd say a new fuel pump ECU is required. Tends to be a problem on aging Soarers with the 1J.