That would be a fairly easy place to start. I carry one of those around in each car just in case. Wouldn't you know, I have never personally had one fail in any car, but I've fixed a bunch of cars where that was the culprit.

From what you've said, you don't hear the pump engage when you turn the key to on (I'm assuming) which is really the only time you'd hear the pump(s, if so equipped) engage.

Given that assumption, there is another menacing possibility, which I have seen only twice, but it is easy to understand why it would create a problem. Sometimes the wiring for replacement fuel pumps is crimped into place... which is fine when the crimp is good, but very bad when the crimp is bad. So, sometimes a bad crimp can cause start/no-start situations, and later the same day there is no problem. I saw this twice with Regina cars, so that may not fit the bill for yours (but is possible).

Also it could be a wacky control unit, but I'm guessing the relay long before the control unit.