I really need more information about your laptop configuration to better answer the question. What operating system is it running? Windows XP, VIsta, 7, Linux, Mac, etc? What OS was on your old laptop and did you use this same setup on the old one or did it have a serial port to connect the RS232 cable?
DOS does not support USB. Windows XP, Vista and Windows 7 do not support DOS. You may be able to run the programming software in Windows 95 or Windows 98 Compatibility mode in these versions of Windows but the USB port may or may not work in compatibility mode because USB was not natively supported in Windows until Windows 98 SE. The USB drivers need to work in order for the USB to serial cable to be recognized.
The Icom F3s is an older radio and so is the programming software. Manufacturers began to phase out serial ports several years ago and there isn’t an operating system that I know of that will natively run a DOS program without some sort of DOS emulation. The F3s has been around since at least 1997 so there is a chance that it may not even support narrowbanding, which will soon be a requirement.