No, the solenoid wire should not affect the ignition system at all. You are talking about the small wire on the starter, right?
Try this to rule out the MSD box.
Jumper the heavy red wire and small orange together and run directly to battery positive. Run the black wire directly to battery negative.
Leave the MSD wires to the coil hooked up, and disconnect the coil to cap wire and hook up a spark plug to it to make the spark easier to see. Make sure the plug is grounded properly! If it isn't you can damage the coil.
Now take the white wire on the MSD and touch it to battery negative. Each time you do this it should spark. Just tap the wire, avoid holding it grounded.
Make sure you run those wires directly to battery to avoid bad connections using iffy grounds on the chassis!
If it works now you know you have a wiring concern to the box.