Any idea what the other black/white wires go to? Is there another light in the ceiling?
all the fans Ive installed , the blue for light kit and black were tied to gether .
I'm no expert, but just installed a fan this weekend. Looks like you only have one switch for both the light and fan. Blue is defiantly the light. If there is a plug in in the room, plug a light in and see if it works if you haven't turned breaker off. If the light works the power would be coming from that direction if not my guess is that power would be running through the switch. You don't want that switch controlling the fan and the plug. Don't let it bite ya or ruin one of the fancy screwdrivers!
Not likely a powered switch to a ceiling box would also control a wall outlet, even a split outlet. That is unless some kluge wired the house.
It doesn't look like those wires were ever twisted together which is the preferred method. The original electrician failed to mark which white was being used as a switch leg. This should have been done with a marker or tape. To find what is what, carefully use a meter and test each black wire to the ground wire. The dead one and the white in the same jacket are the leg. Connect your hot black (power off) to the white leg and color it black. Connect the black leg to the fan lead, which ever you want to control from the wall (either the light, blue, or the fan, black, or both). Connect the white lead from the fan to the white that comes in with the hot black. Connect all grounds together.

Is there 1 or 2 switches? Could possibly be a switch leg for the fan and seperate for the light which isn't all that uncommon. I ran into a similar situation when my sister had me install a fan at her home and previous owners had removed some wall sconces and just put some wire nuts on the wires and covered the box up. Also in another room in her house they ran the feed for the switch thru the J-box so the black wires where the feed for switch, 1 white was switch leg, and the other white was the neutral for the fan, luckily I noticed it before un wiring previous fixture. But like several have stated just grab a meter and see what hots up with switch and that should turn you towards direction of finding where they belong. Also if you aren't that confident in what you're working with ALWAYS take a quick pic. I delete several from my phone on a fairly common basis haha.