I have a Honeywell programmable thermostat and the display is blank. We had a bad storm and the power went out. I have checked the breaker and reset it. The blower will come on when I switch it to ON, but nothing else works. Can someone help?

Try turning off power to Air handler for maybe 30 seconds.
I would change battery in Thermostat.

Thermostat does not have a battery.

Do you have a multimeter? You need to check for 24 volts at thermostat. I have seen transformers blow with storms. Or you may have a 3amp or 5 amp fuse (looks like auto fuse) in the circiut board inside the airhandler. This fuse could be blown.

I have 24 volts at the thermostat.

Did you remove power to Air handler and turn back on?

Check for loose connections at the furnace and thermostat, it sounds like you may have a loose 24 volt or common wire.