I've posted an answer to a somewhat related problem here
but you should read that later as I think you want a better idea of how the whole thing works.
Inside the control box on the generator the power leads get connected so that we have an L1, L2, and N feed wire with L1 and L2 being the 2 "hot" wires. Both of the hot wires pass thru a small current transformer (one wire in each direction) and then go to the various outlets in the output panel. The current transformer makes a signal whenever current is drawn thru either wire.
The current transformer sends its signal to an idle control circuit on a printed circuit board inside the control box. The other wires from this board go to the idle control switch, the power regulator/exciter board, and the idle control solenoid. The idle control board uses the DC voltage it gets from the regulator/exciter to energize the idle control solenoid if the idle control switch isn't in the "off" position and no signal has come from the current transformer for a sufficient time. The idle control solenoid acts to pull the throttle assembly until the throttle bell crank hits the idle adjustment screw (whew!)
Troubleshoot it like this:
1 - Does the engine start at governed speed and then idle down or does it start at idle? If it starts at idle, or seems to idle down faster than usual, something might be amiss in the works.
2 - When you turn the idle control switch to "off" does the engine rev up to governed speed immediately? If not there is almost certainly something ugly going on.
3 - With the idle control solenoid unplugged from the idle control board does the engine rev up to governed speed? If it won't you need to check to see if the plunger is stuck on the idle control solenoid. Some solenoids also have an adjustment that can get loose, check the voltage on the wires coming out of the idle control board if you're in doubt about its being energized or not.
4 - If the generator revs up when you turn the idle control off, but won't do it automatically when current is drawn with it turned on you need to check the current transformer with an ohm meter. Even though this is an AC signal you should mark the leads when you take them off so that they go back from whence they came - it's a noise thing ;-) Little square current transformers in Coleman Powermates are usually somewhere in the 1 - 2 Kohm range, failures are typically that the coil opens up.
Rank me when you've completed repairs?