What was the cause of the water in the basement?

If it was inundated by the storm, for instance, that is a different
sort of problem from a "damp/wet" basement.

My issue seemed to be seepage (we are on the middle of a hill and our
basement is a full eight foot deep and was -likely- never properly
sealed on the outside of the concrete block) so I started with DRY-LOK
on the walls. I am doing it in stages ($100/bucket for DRY-LOC) and
finished a second section this year.

We experience damp floors in high humidity during the hottest Summer
days. This leads me to (hope) surmise the moisture may be atmospheric
- humidity interacting with the much cooler concrete floor - rather
than ground water seepage up through the slab.

When applying the DRY-LOC onto the second section, the wife put on a
thinner coating than had I on the other walls. WE noticed dampness and
mold forming. I re-applied a bleach solution and re-coated that
section the other day with a thick coating and hope that will do it.

The entire basement is damp - evidence rusting on steel tools, sander
belts that snap apart on first use (after storage down there) and, of
course, the moist floor.

There was carpeting on the rear area of the flooring and it did not
appear damp on its surface. But, when I removed it to paint the DRY-
LOC, the concrete started to appear wet when the heat and humidity
increased.

Anything made of wood that is closed up or setting on the floor, shows
evidence of mold - especially where there is no air circulation
(inside my wooden tool boxes, for instance).

A couple of years ago we had two basement specialists come and advise
a trench would need to be dug about the foundation and drainage pipe
and a pump installed to achieve a warranted solution at about
$12,000.00.

My approach will be to continue with the DRY-LOC until all the wall
surfaces are thickly coated and see if there is any change. My idea is
to isolate/insulate the cooler concrete floor from the moist/humid air
with vinyl flooring and, finally, air-conditioning using portable
units as there are but three very small windows in the one end of the
1500 sf basement - no where near enough.

One idea I had was to install ducting from the window-less rear up
through the walls into the attic upon the assumption that the air
would rise up through these ducts/vents via natural convection and
this would afford air movement and help remove moisture.

As to the DURA ROCK suggestion, I thought of that as well. It does not
attract/serve as a medium for MOLD (Hardi-plank/Hardi-board is another
product I thought of. But, then, I was surprised to see mold form on
the DRY-LOC (As I said, think it was not a full coat) and hope the
second coating will fix this issue.

I have heard that raw fiberglass insulation does not support mold
growth - that is the paper backing that does support mold growth. If
anyone has a source to confirm or disabuse me of this notion -
welcome.

Bottom line is that you have to get to the source of the moisture and
fix that first. Then you can consider re-building and the best
moisture-resistant (non-organic) materials for that task.

For one, I will continue reading this thread in hopes of learning what
might be available!

Good luck.