Actually, after you have the database drivers installed, you can copy the ODBC DSNs from one computer to the other by exporting them from the registry in the old machine and importing them on the new one. They can be found under
64-bit Computer
HKEY_LOCAL_MACHINE\SOFTWARE\Wow6432Node\ODBC\ODBC.INI
32-bit Computer
HKEY_LOCAL_MACHINE\SOFTWARE\ODBC\ODBC.INI
Export all of ODBC.INI to a .reg file, copy it to the new computer, edit it in Notepad to make sure all of the paths are still correct, save it and then just double-click on it to get it imported into the registry.
-Dell