If you're using the CT-42A software, it will require MS-DOS and a REAL serial port to work correctly. You *may* have luck with a quality USB-->Serial adapter and running a CMD / DOS window in Windows 7 if you lower the speed of the serial port to 1200 or so. The operative word here is MAY. It may not work, either. Have a look at this page
for info on CT-42A. There's a Programming Help
link there that has additional info that may be helpful, too.
If you decide to try, be sure you can READ the memory of the radio before attempting to WRITE. Understand that the ability to READ is no guarantee that you'll be able to WRITE valid data to the radio's memory. The timings from the multitasking Windows environment coupled with the conversion of USB to serial output can cause the read / write operations to fail, this is why you may have better luck slowing the serial port data rate w-a-a-a-a-y down.
If you use a computer running DOS or Windows on DOS such as Win95, and it has a REAL serial port, your chances of success approach 100%. Even booting a modern Windows machine from a DOS bootable disk with the programming software on it is a giant leap in the right direction, you'll only have to tweak the USB-->serial port settings. If this works, you might consider purchasing an expansion card for your PC that provides real serial port hardware.
Lastly, if it is in your budget, scour craiglist for an old notebook or computer that you can use for your DOS based software needs.