There is actually a difference between a start relay and a start solenoid.
You have a start relay. It has a small coil that pulls a pair of contacts together to provide current to the start motor. It should have a small connection to the coil, that connects to your starter switch. It has two large (usually 3/8" or so) studs, one of which connects to the battery and the other of which connects to the starter. When you hit the starter switch, you should get power to the coil, and that should pull in the contacts that connect the battery to the starter.
A quick test to see if the starter is working is to short the two large studs together. Don't use a screwdriver, use a jumper cable. If the starter spins, then check to see if you get voltage at the coil when you hit the starter switch. If you do, you probably need to replace the start relay.
Put a small lamp across the starter switch (from ign to start) and it will light when the neutral switch is ready to start, otherwise it will be off. I installed such lights because I got real tired of jumping into the engine compartment only to find out that I was in gear. The admiral always thought it was a hoot, tho.
A start solenoid is an actual solenoid that pulls the gear on the starter into engagement with the flywheel ring gear, and at the same time provides the contact for the start motor. I have them on my Perkins diesels, but I don't think you have them on Chrysler engines. Could be wrong....
1975 32' Flybridge Sedan, twin Perkins 6-354 diesels, 1:1.53 velvetdrives, 16 X 19 props. Merritt Island, Florida