In spite of my best efforts--tried it twice--my install of MySQL/PHP/Apache on Peppermint ICE just didn't last. You can read about the steps I followed here.
Though the steps worked, everything seemed to go just fine, both installations failed. At first, I thought it was because I was installing other programs AFTER the initial install. Something, i thought, is goofing it all up. But then, when it died on its own, I realized something else was happening.
This past week--after co-facilitating a Moodle session with colleague Diana Benner-- I had the chance to chat with David in Eagle Mountain-Saginaw ISD and his response was simple: Were you using Ubuntu Server or something else? When I said, I was using ICE, he chided me gently and pointed out that if I go through my steps with Ubuntu Server, it will work.
He then--with support from Ricky--pointed out the same advice Kendall left in the comments of my original post:
sudo tasksel install lamp-server
So, I'm downloading UbuntuServer, and I'm going to give it another shot. I'll probably run the server in a virtualbox, though, since I like my ICE install too much to kill it a third time!