The oil pressure switch and other safeties are not in the circuit while you have the switch in the start position.
Sounds like it could possibly be the starter cut-out switch, Crank relay and or the starter solenoid or starter itself. It could also be the switch itself, but I doubt it. The starter cut-out switch is the one inside of the little oval shaped cover above the oil filter canister. The way it operates is as follows.
It's a centrifugal switch that when you have the engine up to speed, and need to manually flash the field, the switch is open to prevent the starter from engaging and grinding the flywheel. When the engine is not running the starter cut-out is closed and allows the power to energize the crank relay, which in turn energizes the starter solenoid.
I would start by unhooking the connector going to the starter cut-out switch and placing a jumper with inside the connector half going back to the control panel (shorting together the 2 wires of the switch). This essentially removes the switch from the circuit and will allow everything else to work as needed. Move the switch to start and see if your starter engages. If it does your problem is the starter cut-out switch. If not, unplug the fuel pumps so you can hear things happening, and try it again. This time listen for the starter solenoid to clunk. If it does not, then open the control panel and find the crank relay (K3) located about center of the panel on the back wall. There are 2 relays in that location, one of them is K3. Move the switch to start again and see if the K3 relay is energizing, with the panel open you should hear it pull in and make a small clunk.
One of those 3 main components should be your culprit. Any further question, feel free to ask.
