Just fyi, I've read that a bad main/fuel relay on at least some civics will allow the fuel pump to prime but the injectors don't get power.
The end result is the same, no start, but just b/c someone hears the pump prime might not necessarily mean their relay is working.
You could either crank it and pull a plug to see if you smell fuel, or if you've cranked it enough you'll get fuel running out the intake. I wouldn't suggest doing that on purpose but when my coil died it happened, just glad I use upper cylinder lube (plus a lot of oil was getting by the valve seals back then, lucky timing.)
In your case since you don't get the prime, it still could be the relay for all I know, maybe the bad, cracked solder joints on yours happen to affect the pump or maybe your year's main relay functions more like most Hondas :dunno: otherwise the problem could be elsewhere. I was leaning towards the relay shortly before my coil died but if you used to hear a click from the relay and now don't I think you're on the right track. Good luck