Okay, so I have a 1993 Honda Civic LX. 1.5 liter engine, 16 valve, non VTEC engine.
It USED to not start during hot weather and sometimes quick trips to the store (when left in the parking lot). If I were to let it sit again after the failed start for a few minutes, then it'd start back up again. When it fails, it goes 'dug dug dug vewwwwww... ' with a failed whirring sound instead of the usual final burst.
From what I've read on this site, this is generally the sign of a bad relay.
Battery and distributor cap / rotor are new.

Before that, I replaced the distributor and some fuses, which covered previous failures to start.

Anyway, now when I try to start the engine, it makes a higher pitched whirring sound instead of the initial 'dug dug dug VROOM'. Someone told me it could be the starter, so I replaced that entirely. At the auto parts shop they tested my old starter and said it didn't turn over at all, so I figured this would do it. After installing the new starter, it makes a 'whirr whirr dug whirr whirr dug' kind of sound now, like it's trying to catch but the timing is somewhat off. I don't know if this is the flywheel, as I couldn't turn it by hand but when I looked inside the teeth seemed to be in good shape, at least on one side.

However, I still have not replaced the main relay. Does a messed up main relay cause an engine to 'whirr whirr dug' when I try to start it when the starter, distributor cap / rotor, and battery are new? The sparkplugs are several months old, but I wish I could record the sound it makes to post it here. Any advice or help would be appreciated.

Perform tests, in Sections A and B, below:

https://www.askmehelpdesk.com/cars-trucks/faq-how-troubleshoot-repair-maintain-hondas-selected-other-vehicles-46563.html

Hmm, thanks.
When I turn the ignition on, (I did it to position 'II'), the check engine light does come on and then go off after 2 seconds, which is when I hear a click. I'm not sure if I hear the fuel pump run. Is it the 'shhhhhhh' that happens before the 'click'? If so, it's probably working...

When I jumped the Service Check Connector (the two slotted cable in the green rubber coating on the passenger's side?) with a paper clip to check for error codes when turning it on, the Check Engine Light stays on. Like solid on, no flashes or whatever. Then when I take the paper clip jump out, the CEL goes off. This is all while the key is in position 2.

I don't have a multi meter or anything to do the K-Test but I can check the ECM to see if the plate has a spiral blue pattern from heat discoloration--last time I looked at it, it did. Hmm...

Okay, quick update.
I replaced the Main Relay with a new one. Just out of curiousity, took out the igniter unit, checking the distributor cap and rotor for any problems. The unit however, had a yellow wire that was getting caught between spinny parts (my best description for them) and the coating had rubbed off, a huge problem. So I replaced the igniter unit entirely.

Still doesn't start.
Rather, it'll still make that noise. 'dug dug vewwww'... What does that leave? ECM? Sparkplugs? Tachometer? I'm really curious if it's an electrical component or otherwise that would cause my start up to sound like that, a higher pitched whirring sound instead of that rhythmic sparking sound.

. Ensure the timing belt didn't break or slip.

. Replace the coil and rotor, if the timing belt is fine.

All right, so here's what I did.
Did spark test with sparkplugs, they produced a very dim orange spark (don't know if that means anything), but sparkplugs are cheap so I replaced them anyway with new ones properly gapped.

Removed timing belt cover and checked it out. It's good and firm, didn't break / slip.

Ignition coil and rotor are good. I rechecked the sparkplug wires to make sure they were in the right place.

Still won't start. x_x;
I just don't know if it's an electrical problem, or what.. After a crank or two, I smell gasoline. Again, I do hear the relay click and the fuel pump going. When I start it, it still goes 'whirr whirr dug whirr whirr dug'... So what else could it be...

What's your basis for saying the coil is good? I would replace it, based on the weak spark test. You are smelling gas because the plugs are barely firing.

Oh... did you mean the ignition coil? I'm still not too familiar with everything here so I thought you meant the thing that was located in the ignition unit--sorry if I misunderstood.

I replaced the entire ignition unit, and I (perhaps mistakenly) thought the coil was part of it so I felt it should be good.

What does it look like (and whereabouts can I find it)? Thank you.

It's inside the distributor. Here's what it looks like:

AutoZone.com | Vehicle Selection | Year (http://www.autozone.com/autozone/catalog/parts/partsShelf.jsp?categoryDisplayName=Ignition+(Tune+ Up)&fromType=parts&fromString=search&parentId=cat30070&currentPage=1&filterByKeyWord=coil&isSearchByPartNumber=false&navValue=16200027&categoryNValue=16299999&fromWhere=&itemId=prod61181&displayName=Coil+-+Ignition&searchText=coil)

This is likely your problem, since you already replaced the ignitor. Easy job.

So we ran a compression test on the opening that sparkplug #1 goes into... and the reading says... 30. (I was told that it was supposed to be around 92 or something). Checked the other cylinders and it was also fairly low, like the others read 35ish, 40 and 60 respectively. Would that also keep the engine from starting properly? I've read that too much variation could keep it from running well.

Yes, all of the readings are exceedingly low.

Hello you guys. I was reading this thread and it seemed to just cut off.. I'm having a similar problem and I'm trying to read any forums around that could help.. but they all come up shy

Based off what I read so far is that it could be an ECM problem.

If the car decides its going to start. It runs great.. its getting it started that's the problem, it runs smooth when I can get it running. Main relay was re-soldered and replaced, computer was replaced, fuel pump was replaced, battery was replaced..

Starter sounds like its dragging wirrrrrr dg whirrrrrr dg whirrrrr dg wirrrrr...

Last night when I left work it was working like a charm, got to my destination and whe I tried to leave, it had trouble starting at first. I left it alone for a hour or so, went back started it and it hesitated, I gave it some gas on a second try, it caught and sounded a bit rough but then leveled out and ran nice.. its driving me crazy.. the mornings are the worst.. I was supposed to be a work this morning instead I'm doing this.. any thing would be helpful... no one around me has a clue.. not even the so called honda master who may get it running.. but shut it off and it's a crap shoot