Percival P. Cassidy wrote:
Now that we have removed the wet carpet from our basement floor, we can
see a few cracks in the concrete.

Although the recent mini-flood was caused not by water coming up through
the cracks but by water overflowing into the house from a flooded window
well, ought we to fill the cracks before laying new carpet or carpet tiles?

Absolutely. And you should also do a test to see if there is some
moisture coming up through the slab. Put some plastic down on the
slab and tape down the edges. Let it set for a couple of days and
then remove the plastic. If the slab is darker where the plastic was,
you have moisture issues that need to be addressed.

R