Psr-300
Welcome to RadioReference.com!!! First, before running WIN97 or connecting your scanner, plug the cable in to your computer. Go to Control Panel -> System -> Hardware -> Device Manager -> Ports and see if it is listed as a COM port. If it is not listed, you probably need to load the (correct) device driver.
Assuming the cable is listed, open up WIN97. Go to configuration and set it to the same COM port as was listed above. Next, plug the serial cable in to the scanner, and do NOT use that short pigtail they provide with it. The scanner should display "clone mode". If not, there's another problem.
Lastly there are options to communicate with 3 different scanners in WIN97; 2 of which are for the PSR-300. My PSR-300 has v1.06 firmware so I use the option "v1.03 or later". I think that is the most common option. What happens when you try to "download from scanner v 1.03 or later"?