It's actually called the main relay. It could be one of the reasons your car is starting weird. It's a grew box near your fuse box under the left side of the dash. It should be gray with brown near the connection.

Mine went bad once. Car was taking forever to turn over. Ended up being the culprit.

Sounds like you're troubleshooting well. :goodjob:

Here's a link with more details. I did a search on Google.

http://www.tegger.com/hondafaq/mainrelay.html