My blower on my GE combo heater/ac oil fired won't come on auto.

Could be a bad blower motor resistor,mounted by the blower.

It sounds like the AC/Heater blower motor speed controller is burned out, it is located near the blower motor.

Test the electrical circuits ! Manual HVAC or automatic HVAC ?
Do you know the difference ? Heater / A/C blower motor electrical control diffrent . Manual has resistors an a relay for different speeds , automatic has a blower motor control module .Free wiring diagrams here http://www.bbbind.com/free-tsb Enter vehicle info year , make , model and engine size . Under system click on HVAC ,then under subsystem HVAC controls will pop up . Click the search button , then the blue links . First off you need to know what system yours has , manual or automatic.
GMC Yukon HVAC Blower Motor Won Turn On
Blower Motor Problems Auto Repair Help

Depending on the year and model it could be a stuck blower relay.

check the freon there are high and low pressure swithes and will prevent a/c from workin
to protect compressor

REMOVE HEATER BLOWER MOTOR HOT WIRE BLOWER MOTOR IT.IF IT WORKS.YOUR AC AND HEATER CONTROL SWITCH IS FAULTY.CHECK HVAC FUSES AND CHECK BLOWER MOTOR RELAY.IF BLOWER MOTOR DONT WORK WHEN HOT WIRE REPLACE IT.IF ALL CHECK OUT GOOD.HAVE DEALERSHIP DO A DIAGNOSTIC TEST ON YOUR CLIMATE CONTROL SYSTEM.

you might check your switch sounds like to me that your two lower speed sides of the switch maybe burnwed out.

check fuse and switch for heater if good check power to blower motor at heater core if power remove blower motor and check housing for debris (leaves etc)and blower motor for proper turning unit may need to be lubed if hard to turn or seized if seized and oil/lube not working replace blower

heres the electrical diag.....

try to bypass and apply 12v to motor directly, this will tell you if it's the motor or the switch