1. Try installng Money Plus Deluxe Sunset on the new computer. Copy your most current Money (*.mn?) file to your Documents folder on the new computer. Try to Open that file. You may have no problem at all.
2. Can you run Money on the old computer? You might want to consider QIF export from the old computer and import into Money Plus Deluxe Sunset on the new computer. What version of Money does it say you have when you do Help->About in the old computer.
3. Is your Windows 7 the 64-bit version? You might be able to install and run the old version of Money with the Windows 7 32-bit version. Your computer maker might help with going to 32-bit.
4. You could
http://windows.microsoft.com/en-US/windows7/products/features/windows-xp-mode From what I read, you can do 16-bit programs in a virtual XP mode window.
5. I don't know that Money 2004 could read your file. I doubt it.
http://support.microsoft.com/kb/913108/en-us offers the 2004 trial and procedure as an intermediate step to a later version. If that worked, which again I doubt if using Money version 2 or 3, you could then install and use Money Plus Deluxe Sunset
subsequently.
Please tell us what you learn.