Of course it's clear what you have to do -- get everything out of the cupboard, clean the cupboard, and try to trace the leak. Feel all the pipes (they're all dry, as far as I can tell) and then lay newspaper over the floor of the now empty cupboard so that you can check it for damp patches later.
Apart from the fact that all your equipment for cleaning wet and gunky cupboards is in the cupboard under the sink... and that's the most likely location for having an untraced leak of waste water. And all your stuff for cleaning up things that are wet and gunky is all wet and gunky.
Ah. Oh dear.
Welcome to my world.
In other news, the couple of square feet of carpet in front of the cupboard under the sink is also wet and gunky.