Since my original post, I've tried removed almost all NI software (I had to leave LabVIEW 7.1 installed because I didn't have a CD handy.) and reinstalled everything. Now I get a similar error when starting NI-MAX (ModName: mxmax.dll).
I should be able to get a LabView 7.1 CD later this week from one of our other offices. Once I do, I think the next step is going to be to remove _everything_, delete the C:\Program File\National Instruments\ folder, delete all of the Software\National Instruments registry keys, and try a clean install.
Any other tips would be appreciated.