Your TV is working perfectly.
Digital technology pixilates the image if the signal is too weak to build up the intended picture.
TV reception tends to vary in strength during the day - and not all transmitters send out all the channels so your problem channels will just be the weakest - from a weak or distant transmitter.
The reason one TV works fine and the other doesn't will very probably be down to the quality of the signal being presented to the set - cable lengths and integrity of the connectors.
Your license is for equipment CAPABLE of receiving signals - not for tuning in.
The BBC have nothing to do with TV licensing - it's a government agency who contract out to Capita who in turn subcontract to other firms.
You will not get your money back.
Both channels 64 & 70 are owned by CBS Studios International - CBS Action & Horror Channel - the fact that all other channels work OK and these two do not strongly suggests an issue with those particular channels and where they come from rather than the set itself.
With the old analogue TVs poor signal strength caused a degraded picture - people called it interference - with digital transmission poor signal results first in pixilation and then no picture at all.
You will just have to watch those channels on the other TV.
Have you attempted to swap the TVs over?
John Logie Baird, April 2015