Glen,

The moisture you found under the items (buckets, etc.) is evidence that the
floor has probably never been sealed. All cement floors will wick moisture
to some extent and its the sealer that prevents it from getting thru. Use a
cement cleaner and then apply the best concrete sealer you can find for aged
concrete. This needs to be a sealer, a topcoat of some floor paint (that
isn't a sealer) will soon deteriorate and peel.

As for digging up around the garage perimeter - first find the source of the
water. Is it because of a lack of rain gutters or bad drainage (look up
French Ditch).

Bob S.