Protection from a computer on my home network

I have a computer on my home network that it is connected to my router by ethernet. It was given to me by a relative. The administrative account is locked down (no password available or recoverable).  I am a user and cannot install Norton 360.

Are my other computers on the same router with Norton 360 protected?

On each of your other computers, use the Norton Device Trust Level setting to set the the gift computer's trust level to Restricted.  That will prevent the gift computer from being able to access your computers.

Change the trust level of your network and devices