Try this if you haven't done yet:
- Shut down the Mini, probably best by pressing and holding the power button for a few seconds.
- Disconnect the cable to the TV from the Mini.
- Restart the Mini, give it some time for booting to the login screen, or all the way if you have automatic login enabled.
- Then reconnect the TV to the Mini.
Eventually the Mini will detect the TV and login screen or desktop will become visible again.