So after all the fun I had with the MacBook, I eventually found that my MacBook fell victim to the usual MacBook discoloration and random shutdown problems. So did the other MacBook in Exoweb that was purchased at the same time. Last week, we sent the first of them in for repairs with Apple. Guess what the company sysadmin got back as a response from Apple?
"Apple said there's no hardware in the entire world to fix your laptop---they have to manufacture it first. "
So if you're like me and need all these issues fixed, I guess you're going to have to wait a while for the spare parts. At least for me, the random shutdown is limited to once per day, when I work the computer too hard after it has been idle for too long (either in suspend mode or just sitting there unused for several hours.) Once it has shut down once, pressing and holding down the power button for 5 seconds restarts the computer just fine and as long as I keep it busy the rest of the day, the random restarts go away.