My Apple TV stopped in the middle of a movie and now it will not except my password

I don’t want to change my password

That won’t be needed, unless it is too easy to crack, see current requirements.

Possibly two-factor authentication has recently been activated for you?

If you have an Apple TV (2nd or 3rd generation) and two-factor authentication for your Apple ID, then you may be asked to type your password followed by the six-digit verification code directly into the password field. Additionally, there is a time limit, after which the code becomes invalid.

Try this: First enter the characters of your password (do not submit yet), then manually request a new verification code, then append that code to the password (no spaces or other separating characters), and then submit. That should help you get passed the time limit.

What is your model Apple TV? Identify your Apple TV model - Apple Support