You should be able to install Money 2002 onto Windows 7.
Be sure that your Money (*.mny) and backup (*.mbf) files are copied
to a spot that you will have full privileges to, such as Documents.
If they are in a place like ProgramFiles, Windows 7 will create an
impermanent copy of the file for the user to use, unless the user
explicitly right-clicks at launch and choose RunAsAdministrator
that time.
Alternatively, you could install Money Plus Sunset Deluxe if you
are using a US version of Money.
Since you would be upgrading from US version Money 2004 or before
to Money Plus Sunset, see
http://support.microsoft.com/kb/919524/en-us or
http://support.microsoft.com/kb/913108
Those have links to an intermediate trial version that may be required
to do the upgrade.
After you open your Money file on your new setup, whatever version,
change the location to which Money backs up to a location that
exists on the new computer -- typically your Documents folder or a
sub-folder in Documents.