Can the private side of the ring be programmed to perform multiple tasks?
Windows 8 is NFC-enabled, can I use my ring to log into my machine and still use it with an access-control system to unlock doors?
Depending on your method, yes.
Most devices read the contents of the ring and then remember those credentials rather than reprogram the ring themselves.
So as long as you program your own data into the ring and then don't change it, you should be good to go. Just program each access control device after that to recognise what you have entered into the ring.