Engine won't turn over after positive battery clamp came off

I just went down to start my 1995 Honda Civic Ex and first noticed that I
didn't hear the beeps from the alarm.  When I was able to start the
engine, I
opened the hood and realized the positive battery clamp completely came
off
the positive terminal.  I put it back on (it's still loose and the
screw/nut
combo can't be tightened any more than it currently is)  and while I heard
the ignition, the engine wouldn't turn over.
I see the battery and gas tank lights, along with the abs, etc. on the
dash
panel.

The gas gauge is almost, but not quite on empty, which usually means I
have a
few gallons left (the low gas warning light hadn't come on).

Is it possible that the battery is drained because the negative clamp was
still connected?  After the positive clamp was reattached (but still not
tight), I was able to turn the alarm on and off.   When I try to start the
car, the sound of the engine is much stronger than it sounds when one
knows
the battery is completely drained.

I'm going to bring down my portable battery and see if I can start the car
that way.  I just bought this Kirkland battery 2 months ago, and had my
car
repair place install it.