Since the cord is one thing you know you've changed, if you still have the old cord you could try again with that.
However, unless there was a surprisingly high load on the generator (I don't know what it could be though) that sounds like a more than adequate generator. Have you eliminated things like a dirty carb (not run in a while?), bad gas (ditto), and forgetting to turn the choke off (everybody's done it)? Those are the sorts of things which will make the engine weaker than its rating and struggle at much lower power usage.
A guy I know once had low power and high fuel consumption with his generator because the spark plug came loose. It sounded fine with no load, but struggled under load.