I wouldn't replace the switch/control head just yet. There is also a relay wired in between the resistor and the blower motor called the high blower relay. I'm not sure of the exact location on an 88 suburban but it should be mounted inside the vehicle on the heater box, usually behind the glove box. When you find it you can test for power at the dark blue wire, according to the schematic (I can't post a link to the schematic due to this being my first post) with the key on and switch in low or medium fan setting. You can test with a volt meter or a bulb equipped (as opposed to diode equipped) test light. There should be less than 12 volts due to the power being fed through the resistor, probably in the range of 9 to 10 volts, or the test light bulb will be dimmer than normal. If there is power on the dark blue wire check for power on the purple wire coming out of the relay, power on blue and none on purple = bad relay. Hope this helps without having to just throw parts at it.
EDIT- It appears the relay is mounted on the heater box in the engine compartment. I will check on my 88 blazer in the morning to confirm the location.