Hello,I will be glad to try and assist you with this,Welcome to Just Answer.
Since this failure only happens with the new battery it may be possible that the new battery has an internal short in the cells or a bad cell itself.
I have seen allot of batteries that were bad or shorted when they were brand new right over the counter.
The best thing for you to do here is take the battery back to where you purchased it or any parts store and have it tested(this wont cost you anything at one of the parts stores).
If the battery fails then you had got a faulty battery and the warranty should replace it free of charge.
It almost has to be the new battery causing this because your old battery works fine and starts the vehicle.
Let me know if you need anything else,click accept if you feel satisfied with your answer as this is how I get credited for my time,Thanks Pete!