I opened up the fogger and pump and found that the internal spring of the pump piston had broken off at one end. That end held the O-ring retainer that prevents blow-by of the fog juice while the pump is running. Without the O-ring, no juice will enter the heater. This type of failure causes the pump to rattle very loudly when it's running. I was able to repair the retainer and replace the O-ring, and the pump now works like new. It's a pain to do this particular repair, though. I got several pics of the process and plan to disassemble the pump again to get a better set. As far as I can see, this is about as nasty a failure that you can get, barring electrical failures.
For those who may need to replace the pump altogether, I found this pump:
http://www.americandjparts.com/Produ...ine=MINI%20FOG
It looks a helluva lot like the one in my Lite F/X Fogmaster, but without actually getting one, I can't be sure. I'm going to call them tomorrow and see if I can get more info. I'll have pics and such up in a few days.