Where did you purchase the new dongle from Razer directly, a retailer, or separately as a replacement? Is the new dongle showing up in Windows Device Manager? If yes, under which category does it appear? Have you already tried using the Razer USB HyperSpeed dongle pairing utility to pair the new dongle?
In the meantime, please follow the steps here to use the USB HyperSpeed dongle pairing utility and try pairing the mouse again. After running the utility, restart your PC and test if the mouse connects wirelessly.
If the issue persists, please PM me along with the device serial number so I can further check other workarounds. All the best!