Hi, thank you for contacting JustAnswer.com. My name is Russell. I will do my best to provide the right answer to your question.
Take the batteries out of the thermostat again.
Check them with a voltmeter.
Put them back in after 10 or 15 minutes or longer. See if the thermostat shows any signs of life.
If it doesn't, then try cleaning the terminals in the battery compartment, after removing the batteries, first by rubbing off with a fresh pencil eraser, then by wiping the terminals off with cotton swabs moistened in rubbing alcohol, then letting them dry off for 5+ minutes with the battery compartment door open, then try putting the batteries in again.
After that, if nothing shows on the thermostat's screen still, it's probably 'broken'.