Punti 75SX Reluctant to start

My erratic running 96 75SX of which I originally suspected the ECU now doesn't always want to start.
When I turn the ignition on, unless I hear what I believe is the fuel pump
quietly purring, the car won't fire up. The starter motor turns over with plenty of energy but fails to get the engine running.
After quite a few attempts I eventually hear the purring noise and the engine starts. This type of failure first occurred whilst out driving when the engine would cut out and refuse to start for a while. It only dawned on me that the restart was linked to what I believe might be the fuel working its way through.
Any suggestions anyone?
Thanks in advance
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