Basement – Painting basement wall with obstruction

First, make sure you get all (and I do mean all) of the loose paint off the wall. If you get a fairly flexible wallpaper scraper you should be able to bring most of it up. Keep going for that extra 5 minutes after you think you've finished.

Then sand the remaining paint to feather the edges so that they are as smooth as possible.

Next get some filler (spackle I think it's called in the states) and fill in any cracks and large holes. You can also use it over any edges that still seem harsh. When it's dry a light sand will smooth out the imperfections - but don't let it get too dry as it can go very hard.

Then wash the walls down with warm (mild) soapy water, then rinse off with fresh clean water. Allow to dry then prime the wall with either a specialist primer or a watered down coat of emulsion. This will also help find any last imperfections which you can fill and reprime.

Then the wall is ready to paint.

If it's ground water, the issue isn't water vapor, but rather just plain water. Is the water table close or higher than your basement slab? If so, not a whole lot you can do to completely stop moisture issues, as that basement was just built in a bad spot.

That said, the main solution would be a sump pump and drainage tile system. Any water coming up through the earth dumps into the drainage tile, into the pump well, and gets pumped out. Again, though, if the water table is already higher than the basement slab, that'll be a never ending battle as well.

That said, perhaps the issue isn't as much about ground water as you think. Does it get humid in your region? If so, then 'damp' basements are par for the course. Basement walls are usually always going to be cooler than the air, and, a such, will be were condensation forms in a humid environment.

To prevent that, you need to a) dehumidify and/or b) insulate the walls.

A dehumidifier constantly running tends to be a normal part of any basement in a humid zone, so that's a good start. Insulating with walls with XPS or EPS foam will help too, it'll keep the moist air further away from the cold wall.

I can't say if an air exchanger would help or not. If it's including an A/C system, it could help (as the A/C is a dehumidifier) but otherwise I have a hunch you'd just be pumping more humid air into the space.

Products like drylock don't do a whole lot. They're not strong enough to prevent hydrostatic water pressure (high water table) and do nothing to prevent condensation. They're a bit of a gimmick.