Chris, there is one other option that has occurred to me. InfoPath 2007 adds the ability for a network admin to use group policy to remove the ability to connect to external data. If you aren't in Template Part mode, then it's possible that data connections have been disabed using group policy.
Check under the following registry key:
HKCU\Software\Microsoft\Office\12.0\InfoPath\Designer\RestrictedFeatures
See whether you have any of the following values:
DataConnectionAllowed
DataConnectionXmlAllowed
DataConnectionDatabaseAllowed
DataConnectionWebServiceAllowed
DataConnectionSharePointAllowed
DataConnectionDCLAllowed
If you do, then your network admin has likely disabled these features for InfoPath and you should contact them.