Cement board is only needed in areas of direct water contact. You can use green board (also known as MR board) in these areas where you are going to attach the tile board. I would definitely recommend getting the offending adhesive from the tiles off the wall do that whatever you end up doing to the wall you get an attractive finished product.
Now I want to throw this out there. You know that you have a moisture problem caused by poor ventilation correct? If it were me I would identify what is the cause of the poor ventilation is there an exhaust fan that is not working or working poorly? If yes think about replacing the fan. Do you not have a fan? If you don't I would think about getting one and ensure it is sized correctly for the bathroom you wish to ventilate. Also ensure that you vent the moisture OUT and not just into an attic space. The most important thing to problems in a home that is creating damage is to rectify the source of the problem.
Good luck and let us know how it goes. I also think you will get some good insight from the other posters here but take care of the source of the problem prior to covering up the damage.
Where exactly are the tiles? I assume you are talking about the shower and/or tub area?
What are you planning to attach these sheets to?
How much of the old stuff are you taking down? Down to the studs?
Not an expert here, but my understanding is tiles don't fall because of poor ventilation. If there is moisture or water damage in the wall to the extent tiles are falling off, you want to be sure this is taken care of before covering the area or you may hiding mold and rot.
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