I've been having strange Firefox behavior this week, so this morning I decided to trace down the problem I was having (Firefox thought it had an instance already running when I come in in the mornings. I didn't.). Through tracking down that problem, I followed steps to reset Firefox. This turned out to be a bad idea, but as a consequence, I noticed that I too was seeing a problem with my code not even getting into the lines for dojo.require before it bombed. Not only that, but my security certificates files Firefox uses wouldn't let me add Firebug back in again. Like I said 'Bad idea'.
I dug the certificates out of the backup I had and put them in my new profile. Lo and behold, I could get my Firebug added back in, but also my dojo.require was OK again.
If the internal help person who deals with the certificates for the web browsers gets back with me, maybe we'll get to the bottom of this and I'll post our findings.