It sounds like you're saying your basement is heated, but nothing else is (possibly the floor above is exposed to the outside).
What you've done is put in insulation below the subfloor to try and keep the heat in the basement. This is a good idea, however, any time you have warm meeting cold, you're going to get condensation, and so you need a vapour barrier on the warm side only. This prevents the moisture in the warm air from getting into the cold zone.
If you have the vapour barrier on the cold side, you'll get condensation on the vapour barrier itself, between the insulation and vapour barrier, and this will lead to mold (and it's possibly a worse thing to do than have no vapour barrier).
If you have vapour barrier on both sides, you'll also run into trouble as if any moisture DOES make its way in between, there is no drying and no way for it to get out.
If you're using batt insulation, the best thing to do is put a 6mil vapour barrier on the bottom side of the joists, and seal it as best you can around the edges. Ideally you want a continuous barrier with no gaps. The vapour barrier on the ceiling should be connected to the vapour barriers on the walls, and then is typically sealed to the floor using acoustic sealant.
Foam insulation works as a vapour barrier as well, but you need to ensure all gaps between each piece and around the edges are sealed using air-tight tape (eg, Tuck tape).
Realize though that having this vapour barrier in place once you're finished construction will actually be detremental. You don't want to vapour seal between heated rooms, as it inhibits natural drying and air/moisture movement. If you end up having the basement unheated (or minimally heated), then it becomes the cold zone compared to your first floor and so your vapour barrier will be installed on the wrong side.
Since it sounds like it might be difficult for you to get to a lumberyard to build your own solution, you might be better off using a pre-made product. AC-Safe, makes Universal Air Conditioner Supports that might be useful in your situation.
The system requires you to screw the platform into the window sill (which may or may not be possible in your situation), then simply rests against the outside of the building to support the A\C unit.
I've also seen brackets that mount to the bottom of A\C unit itself, and offer support against the outside of the building (but I was unable to find an example online. I think Thermwell makes them).
Best Answer
I don't see that there's anything wrong. Condensation happens... on any surface that's colder than the dew point of the adjacent air. If anything, it's showing that it was worth doing. Despite only being a few mils thick and easily heated, it's much colder than the inside air due to heat loss through the windows. Without it, the windows would be sucking heat out of your house instead of just the interstitial space. The only thing you can do to reduce condensation is reduce the humidity in your house and/or turn the heat up.