First thing I would do is check to make certain there is pressure (Pull the relief slightly), (Hopefully you leak checked it after you filled it?) then I would lay that sucker on it's side and thrash it around for a while to make certain the CO2 is absorbed, do it again the next day or just every time you walk by or think about it. Then I would try a longer tap hose for one, like 6' to 10'. The entire problem may be that it's still warm? You could also just pull the relief until pressure is manageable, then pour one, your natural carb action should maintain enough pressure to dispense, like a cask ale. I naturally carb my kegs all the time but have never served one at room temp.
You could rig a simple jockey box if you have more tubing, otherwise it would take a long time and alot of ice to cool a keg without a fridge, speaking of the fridge, just throw out all the unneccessary stuff from your fridge, like food, milk, etc and put the keg in there. You're still gonna need a longer hose though.