1994 Honda Accord hard starting mystery

[Captain Kickass]

Thanks for taking the time to read this.

My father's 1994 Honda Accord LX (4 cylinder, automatic, sedan) with about 280,000 miles on it is suffering from an intermittent hard starting issue.  Fuel pump, filter, fuel pump relay have all been recently replaced.   However, I still think the problem is on the fuel delivery side.  Normally if you twist the key into the run position, you will hear the fuel pump cycle and then turn the key to the start position and the vehicle fires right up.  When I turn the key to the run position occasionally I will not hear the pump cycle but what usually happens is that after about 15 seconds,  I will hear it cycle, but it is shorter and softer than what it should be, like the pump is only operating at half speed for half the time is usually does.  If I don't hear the pump cycle, the car will not start.  If I do, it almost always starts.  The number of twist and wait attempts required to get the pump to cycle seems to be increasing.  This is just weird.  YOU would think that either the relay would send the signal immediately or it wouldn't send it at all, or the pump wouldn't register that it got a signal or it would detect the signal and immediately cycle normally.  The battery is strong, the starter motor was replaced a year or two ago.

 

This one has me stumped.  Anybody have suggestions for solutions or troubleshooting?

Thank you so much!