Maybe it is using the driver that came with the older unit. I think I would plug it in and find and remove the driver. You can find it by opening Device Manager and expanding the Ports (COM & LPT) section. It will be the Prolific one. Right click on it and choose delete, checking the box about 'Delete the Driver Software for this device'.
Unplug the GPS and restart your computer. Plug the GPS back in and let Windows download the appropriate driver for it.
Note that your Com port may change if this works.