I have been using Remote Desktop for years, so I pretty used to it working
fine, but I am having problems connecting to a laptop that is using a HSDPA
modem to connect to the internet.

In Network Connections, the connections properties shows that File and
Printer Sharing and Client for Microsoft Networks are disabled (not ticked).
The driver installer software for this USB HSDPA modem must have not enabled
these as the laptop is not on a LAN when connected to the internet using it.

Does Remote Desktop need either of these enabled to work?

What else can I look for to see why I cannot connect to the laptop remotely?

ss.