I have a Carrier programmable thermostat that has gone blank. I have replaced the filter and reset the fuse for the furnace. It is still blank. Please what should l do next?

Check to see if 24 volts is going to the thermostat.
Check to see if there is 24 volts at the transformer in the unit.
If battery operated replace with new batteries.
You might also check the furnace disconnect switch near the furnace for 120 volts and that the 120 volts is getting past the switch and into the furnace when the switch is turned on.

Check the furnace door switch, This is located where the blower is located. Usually located at the front of the enclosure. When you take the blower door off you should be able to see the switch. Test the switch to see if it is working.
There are other items but you need to check these first.