Stole a couple of pics from
this thread
On the passenger side unibody section in front of the strut are a few mission critical harness connectors. They are somewhat hidden by the airflow meter and other stuff, so they're hard to see.
Circled in red, the rectangular connector is the power distribution connector for the car.
Circled in yellow, the triangular connector is the connection down to the starter solenoid.
A quick test for a stuck starter/solenoid without going to the back of the starter would be to disconnect the triangular connector. That will interupt the signal from the key.
If it still turns over, it's a bad starter, or there's something funky going on with the little black/yellow wire.
If you have a voltmeter/test light, you can also check to see if there's 12v on the key side of the harness in that triangular connector. (you're checking the black with yellow stripe wire)
That's the signal to the starter, so if if there's power there with the key off, your problems are upstream towards the key.
Here's a pic of the starter side of that harness.
One end of the starter solenoid wire is in that triangular connector, the other end goes to it's own little lug on the back of the starter.