It's very difficult if not impossible to clean a record enough to remove gunge that is stuck in the grooves. Normal cleaning only takes off the surface dirt as all you are doing is wiping the top. If there is dirt that is stuck in the grooves and causing a skip, then you have to take more drastic action to get it out.
Another way which it tried and tested over many years is the warm water method, this can actually desolve clogged grooves. Method is, bowl of warm water, 1 drop of washing up liquid, stir water with finger slowly not to cause bubbles. Soft cloth dipped in water, thoroughly wipe affected record rubbing fairly hard, rinse record under cold tap making sure not to get water on label, dry record with dry soft cloth or paper towel. If it still skips, try again, if that still doesn't cure it, more harsh method is needed as in earlier post.