If the block walls leak (i.e., water comes in) then you need to use a waterproofing paint like "UGL Drylock" This sealer/paint has portland cement in it to seal the wall. They use this stuff to seal swimming pools and the like and it works. If you don't have serious leaks, then you can use a less expensive block sealer (still containing portland cement but not quite as much). Thats what I used to seal the block with because I have no current leaks and it was half the cost of UGL Drylock.
Before applying the block sealer, you should scrub any mildew areas with clorox. And if mildew seems to be a problem, add a mildew inhibitor to your final coat of paint. You say remove old waterproofing??? What exactly is on your walls??? I hope it is not a wax or oil based product that paint won't stick to! Block sealer works best applied to bare block but should also work over a coat of paint. How many coats of paint are on the walls??? 1 or 2 or 50??? Is the paint chiping or flaking off??? Tell us what type of butchering the previous owner did???