If there is still an ongoing moisture problem under your sink, then your sink is still leaking. If its a slight moisture problem (rather than a dramatic noticable leak when you turn on the faucet) then it's probably actually the drainage pipe which is leaking. Fill your sink with water, then check your drainage pipe. If its dry, then drain the sink completely and check the drainage pipe again. If it's is wet after this experiment then its definitely a drainage issue. If so, I recommend tightly wrapping black electrical tape around all the joint-connectors of the drainage pipe and calling a plumber when you have a few hundred bucks available to get it fixed.