Some do some don't.. Of course, Honda makes them very good but $$.
You can try at a local parts supplier but usually electronic/Special order parts, are NOT returnable.
From my experience, Being it so hot down here that they 'go out' frequently enough that Honda usually had them in stock. At around 70$
If you don't have the $, I think there was a good write-up somewhere on this site in the (sticky) that told how to re-solder a main relay to fix it.
Did you check to see if you have enough current to the starter?
I don't know how 'big' you are.. But I usually have to pull the drivers seat (you might find extra money/keys too) to contort myself enough to get my hands up in there to get at that 10mm bolt.
I don't think I EVER bolted them back in.. Just pushed it back up in the area, in case it wasn't the problem.
It's about 3"L x 1"w x 1 1/4H, black, with either a brown/white/black plastic bottom where you plug it in. It controls the main electrics to control your engine so the wires will be larger than most under there going to it.
OK, re-reading your first description:
try and keep the key to the 'on/run' position, get a friend to hold the clutch peddle in, pop the hood, get to the starter, pull little rubber 'boot' off of the +pos terminal on the starter, pull the little wire going to the solenoid, and run a 'jumper' wire from the main lug (starter) to where that little wire connects..
It should turn over. (make sure your girlfriend/wife/?? is holding it to the floor, NOT TEXTING or something) If "nothing", it could be your starter's fried..
E