If you insist on running Windows your options will be limited.
Arm-based single board computers like the Raspberry Pi and the Odroid are very small(only a little bigger than a credit card), take very little power (a few watts) and yet are thoroughly capable of running observatory control software, including schedulers for unattended observations. Even better, essentially all the software required is free.
Sometimes, in my opinion, it is worth going outside one’s comfort zone. An investment of £100 or less will let you explore without breaking the bank.