NTL keeps asking for PID and password to be entered - but it seems not to accept these. Would these have changed in the process of changing the box?
No but make sure you type them in correctly, case sensitive.
As the account holder you can ring NTL to resend you the PID and password, you will need the account number
The WiFi is OK as it works on my friends connection with no trouble. Is he/she using his/her account details/password to log in or yours?