what you probably have on the basement walls is a product called Dry-Loc: an oil based paint that claims to "Lock out moisture". Well, let me assure you that you cannot defeat hydrostatic pressure: it will never give up, it will never go away and it will eventually win and push the paint off the wall. The only solution to a dry basement (from external ground moisture) is to direct the moisture to a low point and pump it or drain it away.
But it sounds like your moisture is not from ground water, but from condensation of excess moisture in your basement. In the summer, warm moist air will collect in your basement where air movement is typically less than your upper living areas and often not circulated with house air with the central A/C unit. This moisture will then precipitate on the coolest objects in the basement which are usually concrete walls, toilet water tanks or window glass. This then becomes an incubater for molds and fungus to grow. To prevent this you must circulate your basement air using your cold air return duct in your basement and/or using a dehumidifier. Occasionally opening outside doors and basement windows will also help, as will letting in as much light into the basement as you can.