Your only concern, really, is your power source : if inverter, cleanliness of output frequency - how close to sine wave vs. square wave, or adequate wattage of your generator to handle multiple loads.
as long as safety switches on the door are intact and not jumpered or otherwise tampered you shouldn't have any issues.
If your only issue is you have power company power but no ground lug then your equipment should be safe to use, but you've eliminated an inportaint piece of safety equipment for YOUR safety.