Air Conditioning - Air conditioner not cooling or dehumidifying

I have a room air conditioner for a bedroom that measures 11 x 12. Every air conditioner I have put in this room doesn't seem to work properly. Currently I have a 5,100 BTU running. The air conditioner condenser cycles on and produces cool not really cold air for about 20 minutes then cycles off and the fan continues for about 45 minutes before it cycles on again. With doors and windows shut, the room is extremely humid. The house is older and poorly insulated. This second floor room gets hot even though it doesn't face south. I have tried several different models and sizes and the same thing happens to each. Please Help!

Is the intake vents on the outside part of the a/c blocked in any way by the window frame, and the outside part is outside right? Not in a crawl space or garage?