I finally determined the source of the leak (How to start investigating the source of this leak in the bathroom), but now I am stuck with dealing with the water damage.
It turns out that the water was leaking from the left hand side of the tank, running down the back of the toilet to the baseboard, and then finding its way to the right where it was wicked up by the particleboard of the cabinet.
I removed the shoe molding from around the cabinet and found mold and water damage:
Do I need to replace the cabinet, or is there a less drastic solution?
Do I need to remove the shoe molding and baseboard to check for damage to the drywall behind the toilet? The drywall sounds dry when I tap it, and the baseboard and shoe molding feel dry, but there are a lot of stains on the shoe molding and on the grout by the shoe molding.