There are many reasons behind water leaking into the basement. It could be a plumbing problem, you may have a larger structural problem with the floor above the basement, you might have bathroom fixtures or even home appliances leaking water and there can be rude surprises as well. You need to embark on a holistic inspection to know what has truly gone wrong so you can fix it.
Making an Assessment
Begin with a thorough assessment of where the leak is. It is natural for anyone to look straight up at the ceiling when there is some water on the basement floor. If you have plumbing systems running under the basement floor, then water can very well leak and rise upwards if there is no other outlet. But in all likelihood, the water stagnated on the basement floor or even the dampness, moisture or wet area could be due to water dripping down the ceiling. Should the damp area be close to the wall or just along the wall, it may not be any fixture above the basement. It could be a pipe running through the wall or any installation adjacent to the basement, either sharing the wall or immediately beyond the wall.
You must know that water leaking into the basement will eventually be facilitated by faulty floors, walls, and ceilings. If you have impeccably waterproof walls, floors, and ceilings, then you will never have water dissipating into the basement and accumulating on the floor or anywhere. You may find damp walls but you would not find leaks of obvious water droplets forming a tiny pool somewhere.
Check the floorboards, false ceiling if you have one, the tiles or dados in the bathrooms, the sealant of the tiles on the floor of the bathrooms, the backsplashes in the kitchen, the various home appliances and bathroom fixtures including the amenities installed on the walls like showerheads and then look for the vulnerable installations. You would obviously look at installations immediately atop the part of the basement where you have found the symptoms of the leak. You should expand your inspection area since water can seep into the floorboards and doesn’t necessarily leak out exactly where it had seeped into.
Water leaking into the basement is a sign of a serious problem. You could fix the valve, whichever it is that is not functioning and allowing water to leak, you may change one fixture or the other that is the culprit here and you can make all such alterations or even upgrades but you have to address the fact that the floor is not completely waterproof so even spilled water will have the chance of leaking through the unsealed and vulnerable floor to the basement.