Yeah, I'd run a drop cord to it to see if it behaves. If you've got an AC volt meter, check the voltage at the outlet under full engine load.
I had one in just last week. The customer reported a lot of smoke, and flames blowing out the stack. The generator was putting out 108 volts at 56 Hz. I readjusted the engine speed so the generator was feeding 118 volts at 62 Hz no load. Put a gun on it, and the engine bogged severely. Checked plugs, compression, etc, and everything was perfect. Put a pressure gauge on it, and he was running 8 gpm @ 4,200 psi out of an 8 @ 3000 machine. Wrong nozzle and improper unloader adjustment was dragging it down. Readjusted the unloader to bypass at 3,200 psi, and it burned clean as new.