That program is about 10 years old but the chances are it can generate a GEDCOMfile (*.GED) that could be transferred to the Windows 7 platform in some manner. As you probable know, the GEDCOM was developed specifically for transferring genealogical data between different programs.
The biggest drawback is that new computers do not come with floppy drives as a standard but there are ways to get around this. It depends on the type of drives that are on the old machine. If it has USB ports a flash drive will work fine.
A GEDCOM file is plain text so images will have to be manually transferred.
As to the new program, the top two are RootsMagic and Family Tree Maker. Both can import GED files.