I have managed to get my PDA working properly with Windows 10.
For transparency when I posted the original question I had upgraded a Windows 8.1 PC to Windows 10, I have since moved to using a different PC that had a clean Windows 10 installation.
These are the steps I followed to solve the problem:
- First of all I installed Visual Studio 2008.
- Then I installed Microsoft Windows Mobile Device Center 6.1
- Then Windows Mobile 6 Professional and Standard Software Development Kits Refresh
- Then Windows Mobile 6.5 Developer Tool Kit
- Finally I opened up the Mobile Device Center, went to Mobile Device Settings -> Connection Settings and made sure DMA was selected under "Allow connections to one of the following"