Yep, that's the starter solenoid alright. Also called the starter relay.
Sounds like you lost a wire/connection/fusible link somewhere though.
If the battery is good (did you test the voltage?), then start with the battery cables and posts. They can look fine and not be. At the very least, pull them off and clean the battery posts and the insides of the cable connectors. If that's been done already, check the cables themselves.
Try taking a jumper, say a 14ga wire, and attach it to the positive side of the battery and the post on the solenoid that it goes to and where the Black w/red wire and it's fusible link attach. Just touching it to the post should restore power if your cable is bad.
Try a jumper from the negative to ground also, just to eliminate the ground cable as a problem.
Next disconnect the wires from the battery side of the solenoid for testing. Does the fusible link at the end of the large Black w/red stripe look bubbled or feel mushy? If so then it's probably blown and you can replace it. But you should first search for whatever caused it to blow.
You can now tell if the link is still good by jumping the Black w/red wire to the battery's positive post. If you have power now, then the positive battery cable or it's contact with the black wire was bad.
You can verify a problem with the fusible link by disconnecting the other end of the wire which is the Black w/yellow stripe wire on the back of the alternator. I know it's a hassle to do all this, but what you're doing is testing before you start replacing things haphazzardly. If when you jump that alternator wire to the battery's positive side all the electricals function again, then the fusible link or wire is bad at the solenoid.
It's all about test and eliminate right now. Sorry for the long post, but hopefully some of that will lead you in the right direction. The system is basically a big loop, with the battery at one end and the alternator at the other. With grounds to complete the individual circuits as needed. And either a positive or a ground (negative) will cause a loss of function.
Good luck.
Paul
