The sign of living in the UK I am thinking Jim!
As a part of the answer to your questions. I too had this ailment with a few things being the main contributors...
My 10mm insulated roof, (20 years old when removed last year) was leaking through the jointing strips and the wooden wall plate was sodden and rotten as a result.
The floor was damp due to moisture seeping through the walls at low level due to earth above ground level being against it.
The door was an old non insulated one (probably interior?) and it's step had rotted away and allowed moisture in.
And them to top it all a whopping great hole into the garage which also has a non insulated up and over fitted.
So, I've had a new roof fitted (by me and my dad) 16mm polycarb'. Very well sealed from the elements!
The earth was removed from the walls and bitumen paint used as far down the wall as I could get and right up the wall too.
The door is now a composite insulated door with weather seal.
and I filled the hole in with 50mm foil backed foam sheets (like the kingspan stuff builders use).
Now after all that I've noticed that even in my paranoid state (of still coating the machines with oil off a rag and or spraying with duck oil) that there is no moisture in there to cause the same annoyance as last year
There have been no drips falling from the roof (it was like raining when you shut the door!!) and I haven't got a heater in there at all!
I Know this stuff is costly... I paid for much of it. Scrounged the rest.
But I think that insulation and protection is your only hope. But till then I'd duck oil the carp out of every machine bed while you're not using it..... Trouble is you have to wipe 'em down when you come to use them next time!
Personally I would not open the window, I would think that'd let more moisture in? Fog/mist etc (we've got plenty of that!!)
The de-humidifier I'm not sure. Couldn't hurt I suppose But might be costly running etc?
I know, probably not much help, but it's what I know.
Ralph.
P.S. When you come to sort out the garage door ask me for details and the likes.... you live too far away for me to help with the fitting but I'll sure give you Impartial advise so you don't get ripped off