Good try shee, the problem with that is that things that slip under load might work ok with it jacked up off the ground.
Reed, have someone else try to ride it and, like Phraple said, look for where the junction is between what moves and what doesn't. Power transfers through parts in this order> chain, sprocket, sprocket hub, axle, wheel hubs, wheels/tires. If you see slipping at the junction between the sprocket hub and the axle, then as others have suggested, there is a problem with the splines between the two. This is the most likely simply because one of the weakest points. Aluminum hub on a steel axle. Missing/damaged teeth on the sprocket is also highly likely.
Remove the chain from the sprocket, remove the two large axle nuts, and slide the hub off to visually inspect. Note, I didn't mention removing the wheel hubs or wheels because to inspect it you just need to move it over, but to replace do this as well.