Honda ems 4000 generator starts and runs great, but no power

Question re-written to get rid of abbreviations and put things in correct order.

You don't give a model number of the generator or the engine model number. Typically a 4,000 watt Honda Generator has an 8 H.P. 4 stroke air cooled engine.

https://www.google.com/search?q=Honda+4%2C000+watt+Generator%2C+how+many+H.P.

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Some breakers will not reset nor turn on when defective. Sometimes pumping them off-on works.
Has anyone got in there and wired them wrong?
Check their wiring and bench test the breakers if needed.

sounds like a fuel flow problem.Pull the fuel line off at the carb and see if fuel flows well when you turn the gas on.If the fuel is flowing to the carb,you will have to remove the float bowl off the bottom of the carb and check for fuel flow through the needle and seat which the float controls in the carb.If fuel flows well through the needle and seat and the float words well without binding, next is to clean the main jet which may be plugged.Ethanol in the fuel these days can cause problems in these areas.ALWAYS shut off the fuel in all small engines and let the carb run dry when storing small engines for any length of time.

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Generator Set Diesel Generator Cummins Volvo Perkins Generator

I would say the AC is overloading the Generator. AC units require ALLOT OF POWER.

Only specs I can find

AUTO. AIR CONDITION
CEILING VENT. POWER
CRUISE CONTROL
GENERATOR 2500 WATT
GENERATOR 4000 WATT
GENERATOR 7000 WATT
HYD-LEVELING JACKS
ICE MAKER
MICROWAVE OVEN
REFRIGERATOR 6' OVER BASE 4'
ROOF AIR CONDITION
SPARE TIRE W/ RACK AND COVER
STEREO RADIO W/ CD PLAYER
TV SATELLITE DISH

yes it sounds like the solenoid is sticking

Crankshaft and Camshaft Position Sensors Camshaft Position Sensor Engine timing is determined from the relationship between the crankshaft and camshaft. This relationship is maintained by a timing chain or timing belt. The Engine Management System does not control engine timing but it does monitor the relative position and speed of these shafts by monitoring signals generated by sensors. The Engine Management System (EMS) uses signals generated by the camshaft position sensor to synchronize fuel injection to the valve sequence and for the on-board diagnostic procedure for misfire detection. The EMS energizes the injector at or near the time the intake valve opens. For misfire diagnosis, the EMS compares the number of camshaft sensor reference pulses and the number of crankshaft position sensor reference pulses received. If the EMS receives an incorrect number of pulses Diagnostic Trouble Codes (DTC’s) should be stored in the EMS.
If the camshaft position sensor or circuit is faulty most engines will start. Some engine management systems will then default to a pre-programmed injector firing sequence. All injectors may be energized simultaneously or all of the injectors on one bank may be energized at the same time. If the CMP data is required for misfire detection and reliable CMP data is not present misfire detection would probably be suspended.
Related Symptoms The following symptoms can be caused by an intermittent wiring connection or faulty signal to the EMS:

• Extended crank time with a cold engine
• Intermittent rough running
• Unstable idle
• Bucking
• Hesitation
• Stumble
• Chuggle
• Poor fuel economy
• Stalling on acceleration

Crankshaft Position Sensor Engine speed is a very important input to the Engine Management System (EMS). Crankshaft speed and position are the basis for many calculations made by the computer. Crankshaft position values are transmitted to the computer by pickup coils also known as Permanent Magnet (P/M) generators, hall-effect sensors or optical sensors. The Crankshaft Position Sensor (CKP) also known as engine speed sensor is located in close proximity to the crankshaft.
In addition the EMS uses minute variations in the CKP sensor data to determine engine misfire. The EMS uses this information in conjunction with the camshaft position sensor to perform misfire diagnostics.
Related Symptoms: No Start/Intermittent Start Condition – Can be caused by a faulty crankshaft position sensor due to loose connections, bad grounds, high resistance in the circuit, or opens in the circuit

The wiring diagram for the generator is pretty simple. You have three wires coming out, White/Green/Black. The black is the Hot, White is neutral, and green is ground. If the generator is running and you do not have power at the black wire, the problem is in the generator. Check the circuit breaker on the generator for OK. Make sure that power is passing through it.