I don't know if this applies to 2010 RAMs with manual AC, but manual AC controls used to be controlled by engine vacuum lines. If you move the switch to one position, the switch manually moves/diverts the vacuum to a set of ports, and the ports apply the vacuum to the vent diverter (it pushes/pulls the diverter to the appropriate position to cause air to blow through a set of channels). There is also a "recirculate" control - if you put the control into recirculate, does air still blow through without the fan being on? If this is a manual system that is vacuum controlled, then you have a vacuum leak most likely. You should be able to tell if you pull the console - if you see plastic/rubber tubes that run to the AC faceplate, you'll know it's vacuum. Check that they are lined up correctly and not disconnected or the ports broken on the back of AC control faceplate. If it's electrically controlled, then there's an issue with the power supply or ground and you'll need to do further troubleshooting - start by checking the fuses. Air will blow through system if you are NOT in recirculate because the vent from outside of the vehicle is not closed. As for the fan - it sounds like the fan switch is bad - there are a couple of resistors inside it that control how much electricity goes to the fan motor - in high speed mode, almost no resistors are used, but as you decrease the speed, more resistors are in the circuit, which causes less voltage to be provided to the fan motor. While you can't replace the resistors, you can replace the entire switch. You should be able to replace that yourself - but it COULD be the fan motor has gone partially bad (not likely though).
