Just a thought, do you see signs of water in the area of the walls?
If the cellar was dry before you bought it, (OK), then something you did may have caused the problem. Nailing into the cement floor, could have caused cracks to have formed in the floor and now lets the moisture though.
Note* I had a dry cellar once for three years, then we had a week of rain and I had 4" of water! It was a damp basement up to the time I put it on the market!
I think you do need a pro for this work. It is not worth the headaches to go through it again.
My only other concern is when you get this fixed, do you have a legal (ie. SAFE) egress to the outside world from each bedroom?
Also, a hard wired, battery back up, smoke detector in each bedroom? You should have had one in a common area in the basement anyway but you do need to have one in each bedroom.
Where is the furnace/boiler located and where is the "make up" air coming from?
The make up air for a furnace/boiler can not come from a bedroom. I would get a carbon monoxide detector for each room.
The people here will tell you, bedrooms in basements are my bigest nightmare.