1996 Ford Mustang Won't start unless jumped?

I have a 1996 Mustang GT. Every once in a while, I would get in and try to start it and it would go "CLICK" and nothing else. Would have to get out, undo the NEG terminal, brush any corrosion off and put the cable back on and tighten the cable and it would start.

Now yesterday after work, the car did the same thing. Did the usual as above, but nothing, just a fast click, click, click. Figured maybe I left something on. Had a friend jump the car, started right up. Ran it for 30 minutes, turned off the car, wouldn't start again, just click click click.

Came home, bought a new battery. Put it in, wouldn't start, click click click. Figured it was a not charged battery, so I jumped it with a "power boost" and the car fired right up. Went for a 12 mile ride, about 25 minutes, came home. Shut off the car, wouldn't start. Put the boost on it again, and it started right up.

Took the battery charger and put it on the battery for 5 hours this morning. Went to start it afterwards, nothing, but fired right up after I connected the "battery boost" to it.

Also, check with volt meter when car is on, Battery is at 14.05 volts, on a load it is at 14.01-14.03. Turn it off, the battery is at 12.9 or so (which with the test connected dropped.1 every couple of seconds from 13.8 down to about 12.8 when I stopped checking).

Could it be possible the neg cable is bad or has come loose under the car? If that is the case, were does it connect under the car? I followed it up top until it ran under the engine, but it was pouring rain and I didn't feel like crawling around in the mud.

Thanks for any help!