It's doubtful that you "fried" the starter solenoid. Make sure the battery is fully
charged and that all of the cable connections are clean and tight. Your solenoid
(actually starter relay) has 4 terminals. The large terminals are Battery+ and
Starter. The small terminal closest to the Battery+ cable is the Start terminal. The
small terminal closest to the starter cable is the Bypass terminal. (it supplies full
battery voltage to the ignition while cranking).
 To test it:
 1). Jumper the Battery+ terminal to the small Start terminal, the starter should
engage. If so the solenoid is working properly add the problem is in the wiring from
the ignition switch. If not:
 2). Jump across the Battery + terminal and the Starter terminal (both big ones). If
the starter engages the solenoid is likely bad. If it doesn't engage, the problem is
in the starter itself.

 Why are you trying to rig a switch for the AC compressor? There is only one switch
in the original circuit, on the heater\AC control head. Power comes from the ignition
switch, through the AC switch, to the compressor. It shouldn't be difficult to repair
it. IIRC, the AC switch is available as a repro.If not, check E-bay. Your 66 is a nice
car, I've had 3 of them. Galaxie fastback, Galaxie XL, and currently a 7 Litre. I'd
like to see you do it right and am familiar with these cars, so If I can be of
assistance let me know.