We had a power failure for couple of seconds two times in one night and I noticed the display of my honeywell T8001 was not showing the temp/time and was showing all possible symbols that can be displayed on it. I thought it is dammaged but when moving to fan it works but does not show anything on display. Please advise.

Not a lot you can do here. I would try replacing batteries first. If this doesn't help, I think you may need a new thermostat. How old is it, it may be under warranty. If fairly new, take it back where you got it and see if they will replace.