Might be something wrong with your SMC or thermal throttling going on. Either way I'd suggest resetting the SMC and if that doesn't fix it check out Activity Monitor to see what's wrong.
I had a old Air which ran very slowly and fans spinning like crazy due to a issue with the cable from the keyboard/touchpad. Apparently if the SMC does not get proper signals it will go into a "failsafe" where things work but slowly.
Probably not the same issue, but just a little anecdote on a similar symptoms caused by different issues so that nobody gets tunnel vision on the battery, which might very well be the cause in this case.