Gas and Oil Home Heating Furnaces - Lennox fan/limit switch

Furnace/Air conditioner is Lennox Pulse G14. Just replaced thermostat. There are 5 wires thru wall, however Termostat works only as 4-wire with jumper.
Furnace runs and heats. However starting abut 24 hours after replacing thermostat furnace blower motor is erratic. Sometimes it cycles normally and all is well. Other times I hear a "buzz" coming from furnace which sounds like a relay is stuck or blower motor is trying to "kick' on. If I switch furnace blower swith on thermostat from automatic to on the "buzz" gets louder. If I switch the blower switch back and forth several times the "buzz' stops AND the furnace goes, once again into normal operation. Somestimes the furnace will run normally for several hours and through several on/off cysles AND THEN the "buzz" begins again. I have waited to see what happens and after a few moments the "buzz' stops. Can anyone suggest my next step. I have not removed the upper panel cover to determine the fan/limit control, relay, circuit board, etc.

What type of t'stat did you remove and wire designations? And what type of t'stat did you install and wire designations?

Thermostat removed was Honeywell Programmable Thermostat/32 and replaced with same. Hooked up as per 4/wire Heat/Cool (jumper intact) illustration on page 21 of "Programming and Installation" Instructions.
white to white terminal, yellow to yellow terminal, and green to green terminal. 4th wire to R terminal . Jumper from R terminal to Rc terminal. Hope this answers questions.

Make the relay buzz and find it's exact location. Need to know whether it is the blower trying to come on or wether it's a relay. t'stat sounds fine. You may have blower problems or relay.

If you remove the top panel access door to the main furnace compartment you can see the gas valve, ignition control, etc. Above the main cabinet compartment is ductwork. The buzzing seems to be coming from there. If you lay your hand on the ductwork you can feel vibration. I can see a Honeywell "box" mounted on inside of main cabinet that I assume is the Fan/limit control. The sound is not coming from there.
The furnace cycles on and off and sounds like all is well, EXCEPT the blower does not kick on AND when one puts the blower thermostat switch from auto to ON the blower does not start to run. The Thermostat instruction manual and the furnace manual say the blower should run if the Thermostat blower is switched from auto to ON.

Sounds like your Blower Motor is going up... or the start Capacitor... kill power and see if you can turn blower, it should turn freely and spin for a bit...... if it does try spinning and turning on power, if it takes off then you need to change the Capacitor...

Thanks. Blower turns freely. No smell. No hot spots. Capacitor not not to touch. Holding door panel switch in and turning blower motor by hand DID NOT START motor. With some anger (as house temperature was now 52 F) I shoved lower cabinet panel door back in place and VOILA the blower motor began to run. I went back to thermostat and turned blower switch to auto and the furnace began to run and continues to run. Temperature in house is now up to 65F from 52F and furnace pulse has cycled and recycled normally several times. I am waiting for the temperature to reach 68F to see if the furnace cuts of and then comes back on when the temperature decreases. SOMETIMES the simplest things cause the biggest problems. I guess I must not have placed the lower cabinet door on properly to actuate the switch. DUH!!!!! What do you think. Thanks for all your help. I hope this is a final reply other than additional thanks.