First of all that's a great site and not just the main relay page.
I was going to recommend it myself, primarily for the great pic of the relay location(s), after I replaced the main relay in my car so I'd have some insight to add but haven't gotten around to that yet.

Regarding the OP's problem, if the main relay was acting up the engine would still turn over. It wouldn't affect the starter.

I'm thinking the problem could be the ignition or a fuse(maybe one of the big ones under hood, just a guess). The ignition is a relatively common problem on some gens/years as they get older.

I wish I had time to look into it for you but I gotta go.

It might help to give the year (I assume it's a civic), etc. so the more knowledgeable and well-rested members can help