Last night my furnace began making screeching noises, which kept getting louder and louder. We took the face off the furnace and it stopped, but we also have no heat. Is this an easy fix or a sign my furnace is dying?? Help!

Most likely just a bearing in the motor. Try turning the blower by hand. If you get the screech or it feels rough, pull the motor. Take it to an electrical supply. If they have a shop, they may just replace the bearing. Otherwise a new motor should fix the problem. If the wires aren't on a plug to the control board, make careful notation of how they are connected. Many motors have several leads giving different speeds to customize to your HVAC system.

Could be either a draft inducer motor if it has one. Or the blower motor. Either will probably require a service call. If the furnace is over 16 years old it may be time to look into replacing it, as either of those repairs will not be cheap and you will continue to have breakdonws due to the age.