First, my sympathies to anyone who still has to deal with Paradox databases. I recently setup Microsoft Access 2007 on a Windows 7 64-bit computer to manipulate data in an old Boreland Paradox database (from a limited user account). I consider this to be the computer equivalent of putting the engine from an old VW Beetle into a new Porche 914 (rather than the other way around)... but nonetheless, it has been done. The only serious problem was the following error message, which appeared upon opening the database from Access:

The cause was a series of permissions errors caused by the more strict access controls in Windows Vista/7. To fix the error perform the following steps:

1. Grant write permissions for the user/group who will be running Access on HKEY_LOCAL_MACHINE\SOFTWARE[\Wow6432Node]\Borland\Database Engine\Settings in the Windows Registry.
2. Change the BDE configuration to avoid writing to C:\PDOXUSRS.NET
   1. Run "C:\Program Files (x86)\Common Files\Borland Shared\Bde\BDEADMIN.exe" as an Administrator
   2. Navigate to Configuration | Drivers | Native | Paradox
   3. Change the NET DIR parameter to somewhere writable (and shared between users). I created a folder in %systemdrive%\ProgramData.
3. If necessary, grant write permissions on HKEY_CLASSES_ROOT\.html in the Widnows Registry. I don't believe this was strictly required, but at one point I had enabled it during testing and am not completely certain if it was ruled out as a cause of the problem.

After performing the above steps, the error should be resolved. If not, I suggest using Process Monitor to look for permissions errors and attempt to resolve them (which is what I did). Best of luck.

Additional Information: Also, for those looking to the future, Access 2010 and later have dropped support Paradox 3-7, so further workarounds may be required.