Hi all with my 1997 2 litre petrol car I have a problem with the starting sometimes

When I turn the ignition key and hear the fuel being pumped up to the engine I know the car will start straight away

When I dont hear the fuel I know it will not start Sometimes I wait an hour sometimes days I thought fuel pump relay but that is fine Has anyone had a similer fault and more importantly has any person solved the problem as my wife wont drive the car so it just sits there