New iMac mouse & iPad not responding

Hello, martymmm.

It may be that the new devices need a bit of a recharge. Plug each into the powered-on Mac with the included lightning cable and give them 30 minutes or so.

Also, make sure that you have switched them on. There will be a green color (not a light) behind the switch when they're on.

Connect an Apple wireless accessory with Mac - Apple Support:

https://support.apple.com/guide/mac-help/connect-an-apple-wireless-accessory-mchlp2656/mac