Ok, I figured out what the problem was. I'm on a Windows 2000 machine with two users: Administrator and me. I development my application as myself, in the Users group. To install NI-DAQ 7.1, I logged in as Administrator, uninstalled the old, rebooted, logged in again as Administrator, installed 7.1, rebooted. I then logged in as myself and tried my VI, getting the above errors.
To test, I logged in again as Administrator and tried running my VI. It ran flawlessly. I then logged out and back in as myself and tried my VI again. This time, I got no error messages.
So it seems that when using NI-DAQ as a non-priveleged user, it must be started once as Administrator before it can be used by a regular user.
This should be considered a bug, or at least a p
oint for further documentation during install.