Sorry i edited the post and I don't think you saw it. It definitely could be the solenoid. You won't know that until you take it out and test it.

The starter solenoid is part of the starter. The solenoid contacts could be worn inside. I'm not sure if your specific starter has contacts that are easily replaceable.

You can try the caveman test with the help of an assistant. Have the assistant hold the key in the start position. Tap on the starter with something like the handle of a screwdriver with medium/light force. If the starter fires up, you pretty much narrowed down the issue to the starter or possibly the electrical connection on the starter.

If you go with an aftermarket unit, I recommend Denso. You may have to purchase online. I've seen numerous posts on here about failures on remanufactured parts you can get at auto parts store.

Haha I like the caveman test... I'm pretty sure that it's the starter solenoid at this point, and it looks like it is part of the starter, so I'll just order one. Thanks for the recommendation on Denso!

Yes the solenoid is attached to the starter but can be replaced separately. That is up to you and the funds you have available. Denso is the OEM for Honda starters and would suggest that as well. Remember all starters at this point in the cars life are remans. Me personally I would replace the whole starter to make sure nothing goes wrong later.