If the cables are corroded at the battery, then yes, you can get a jump and the car will run. If cables are corroded on the other end, then no, a jump may not work.

When you turn the key you say you here a loud click, then no turn. But can you hear the starter trying to turn? Do the lights dim? What your saying does sound like a bad starter. But before you go and get a new one, I would suggest pulling the + cable from the starter. Remember to pull the negative from the battery first. Clean up the connection real good and put back on the starter and see if that helps. If not, get the starter tested and replace if needed.

Dan - I took your initial advice and went down to my car with a vice grip, a socket set, a can of WD-40 and a ball of steel wool. The bolt on the (-) came off easily but the nut on the (+) side was almost rounded off so I had to inch it off with vice grips. I sprayed both the bolts and the terminals with the WD-40, then scrubbed both thoroughly with the steel wool.
Connected the battery again, tried starting the car, and we have LIFE!

It ran for about 45 seconds, then shut off on its own. No power at all.

If you go back to my initial problem, I was having intermittent battery connectivity problems. Following this rationale, I went and wiggled the (+) cable and I heard the key chime come on. Went and gave the (+) cable another shake, gave the corresponding nut one last twist with the vice grip, started it again and I was able to drive it the 1/2 mile home. Which, considering it was on a city street and we're expecting 3-5 inches of snow in Milwaukee, was a huge blessing.

So, THANKS! Your advice is golden!

And at this point I'm convinced once and for all that all I need to replace is the (+) battery cable. Which brings up my next question...
The (+) cable splits into two lines: One goes to the base of the engine (to the starter?) and the other appears to lead into the firewall somewhere... Where?
How do I get to the other ends of these cables??

Best,
-Chuck.