The Wireless Comfort Keyboard 5050 connects through its supplied USB receiver and does not support Bluetooth pairing.
I’d first check whether the receiver is still plugged into your old computer >> move it directly to a USB port on the new computer >> wait a moment, then try typing.
If it still doesn’t respond, try another USB port and fresh AA batteries.
Do you still have the original USB receiver? Let me know how it goes, and I’ll help with the next step.