HOW TO FIX: "Remote Desktop Connection Broker" service not auto starting after reboot.

STEPS:

- Connect locally or from LAN to your RDS server.
- Start "Services.msc" and find the service "Remote Desktop Connection Broker"
- Double click to open properties.
- Switch between Automatic and Automatic (delayed start) and back to Automatic.
  Also check under dependencies tab that extra services are listed in startup.
- Finally right click start button and choose Run.

Restart and check!

P.S.
If after restart the "Remote Service Gateway" service hasn't started apply above process.

Good luck!