I have a new home 1 yr and when the furnace kicks in, I am assuming the fan it makes a noise but as soon as the heat starts the noise is gone, could this be the furnace blower

You did not post the make and model number! You said you replaced the fan? The compressor and motor for the fan both use a start capacitor.

If you have a gas or fuel oil furnace, that is your igniter trying to light the fuel. If it does it for a few seconds and quits without lighting the furnace, there may be no fuel getting to the burner. Check for fuel supply - oil tank empty? gas line turned off? etc

Depends on the cost to repair. Probably a 22 year old furnace is not very efficient also. Take every thing into consideration.
If it still works it may work for a while but you don't want a break down in the middle of winter.

Coleman furnaces us a temperature delay with a temperature on around 130F to 150F and off around 110F.

If the inrush of cold air cools the delay below the off temperature the fan will go off until the heater heats it up to the on temperature.

pls send me snap of your furnace controller , i can help you

It wouldn't be stuck if that's the case the valve would never shut off. Sometimes those 2 stage heat thermostats stats call for 2nd stage if the room temp drops more than 2 degrees. Easiest way to check is take the w2 wire off of the tstat and try a call for heat. If the furnace kicks on both 1& 2 stages then its either your wiring on the fan board or a dip switch setting. If it kicks on 1stage then it's your thermostat.

what make of furnace check for birds and blockage
unfortunatley when they go there gone the squirrel cage wheel will not come of shaft u will need motor n wheel or a "plug n play housing all in one"

Have you confirmed that the thermostat is programmed correctly?

Did the thermostat ever control the temperature of the house properly?

When you indicate "kick", are you talking about flipping the Auto-On switch back and forth? The Auto-On switch only controls the fan, and no heating or cooling (Auto - fan runs on call for heat or cool, On- fan runs all the time.).

If "kick" means making the heating work, and if you have the same problem for making the cooling work, chances are good you have bad thermostat.

If the problem only occurs with the heating, and cooling works fine, then the problem could be in the controller board of the furnace, assuming you have a more recent (1990's or newer) furnace.

when was last time furnace was serviced --air filter change burner area cleaned vacuumed the hum can be a few reasons ---fan bearing need service [ oiled ] fan bracket bushings damaged or loose --burner out of adjustment burning improper etc these are a few