As with all small gasoline engines there is a gas tank, oil reservoir, spark plug, carburetor and piston. The piston action drives a shaft connected to the electrical motor to generate the electricity. If the engine will not start or run erratically, start by checking the fuel and the rubber fuel line connecting the gas tank to the carburetor. Water in the fuel will prevent operation and is very easy to get into a small engine gas tank.
Check the fuel line for any blockage preventing adequate fuel flow. Open the cover to the carburetor and make sure the choke properly adjusts the inlet valve (a rotating flap allowing air and fuel in to the cylinder.) Remove the spark plug and check the anode (a wire close to a metal post) for fouling from oil and carbon buildup.
Finally, the Coleman Proforce generator has an on/off switch that allows the engine to run and shuts it off. Check to make sure the wire leads from the switch to the engine are not frayed or disconnected.
If the engine runs but there's no electricity, first check the fuse. It is located on the face of the generator behind a small cap. If the fuse wire is burned through, replace it with the same-size fuse. Don't assume a bigger fuse will handle more load. It will just allow more electricity to flow and can damage the electrical socket or what is plugged into the generator.
The Coleman Proforce generator uses sockets just like wall sockets in building. Remove the socket and inspect the openings. It's easy for dirt and other contamination to get in the socket and prevent contact with the installed plug.
Finally, check the shaft connecting the engine and generator motor. If it is not rotating when the engine is on or not fastened properly to the motor, then there's no power generation. The shaft can become loose at either end.