Yeah no problem using your existing pass on your new box, just sign into the new box with your existing account details where you can have up to four devices on your account with two simultaneous streams.
Out of curisoity is there any error code or message showing on your existing box that can't connect to your WiFi have you tried the normal steps of rebooting both your box and router ?
Also have you tried factory re setting your old existing box, by pushing a pin for about 30 secs in the small reset hole on the back of the box ?
Have you got the white box or the black box ?
If you have the black box and if practically possible have you tried an Ethernet cable between your existing box and router.
Also, I am guessing you have tried to disable the network pings on the box by following these instructions below ?
Should have also added have you tried switching off the router off at the power switch for about 20 minutes and then power the router back on again where it should then automatically find the best WiFi settings.
Also, make sure the NowTV box is well clear of any obstructions and move the box in different positions on your TV shelf to see if there is any improvement with the WiFi.