Cannot establish connection

Windows 8.1, free license for the home machine.  Windows 10, free license for the remote machine.

I am writing because the computer I used TeamViewer to check on from home blew up.  I replaced it with a new one, installed TeamViewer 13 on it, logged into the account...and have been having boatloads of grief trying to access the remote computer ever since.  Tons of following Emails to establish trusted devices, and still nothing but "A connection could not be established."  Could you please tell me how to get everything back in order again - even if it means having to wipe out the accounts on both machines and start again from scratch?
Thank you very much for your time.