If you have a 2nd or 3rd Gen ATV (you said it was old) there is no area to enter numbers, after you’ve done the password
Please Identify your Apple TV model
You put in your email - submit- then add your password with the code right on the end of your password (no spaces) altogether as one entry - then click submit
- email- submit
- password123456- submit
If you don’t have the older model and the code isn’t being accepted, you are taking to long once it’s sent to you. (It expires)
If you need more time to have the code sent to you:
Get a verification code and sign in with two-factor authentication - Apple Support