Wet Vac whatever you can get out of it and turn the heat towards the floor for a while but if its as wet as you say you will probably need to strip the carpet back.
Run some insulation tape along bottom of the window where the glass goes into the rubber to stop some of the water getting into the door panel.
Go onto ebay and get some of the butyl rubber seal to fix the door ASAP, you will be better fixing the problem before you start to try and dry the floor out
Aha! A wet vac, why didnt I think of that?? I assume a Henry isnt a wet vac . I searched ebay for the "butyl rubber seal" and got no results?