My starter button does not light up, but the other lights are flashing

Here is a list of refrigerator manufacturers and how to reset the filter change indicator light:
Amana- Press and hold the Auto and Dispenser Lock buttons until the water filter status indicator light flashes.
Frigidaire- Press and Hold the Reset Button Until the Indicator Light Flashes.
GE General Electric- Press and Hold the Reset Button for around 8 Seconds.
HotPoint- Press and Hold the Reset Button for around 8 Seconds.
Jenn-Air- Press and Hold The Water and Lock Buttons until the Water Filter light flashes.
Kitchen Aid- Press and Release the Light Button 5 times Quickly.
Maytag- Press and Hold The Light and Lock Buttons until the Water Filter light flashes.
Samsung- Press and Hold the Ice Type and Child Lock Buttons at the same time for 3 seconds.
Whirlpool- Press and Release the Light Button 5 times Quickly.

Its probably the cleaning light that comes on periodically to remind you to clean the unit. Shut off the unit AND when you do so hold down the power button for several seconds until the flashing red light shuts off. The cleaning light should stay off until the next cleaning is due.

Per the Air-O-Swiss FAQ:

Q: Cleaning light is flashing (AOS U650, AOS 7135, AOS 7142, AOS 7144, AOS 7147)
A: Switch the unit OFF and unplug it. Empty the water in the base. Rinse the base with hot/clean water. Do not submerge the base! Visually inspect the base for dirt or mineral build up. If soft water is used decalcifying the unit every 4 weeks with EZ Cal is suggested. If hard water is used the unit should be decalcified every 2 weeks. Do not forget to reset the clean light after resetting the unit.

Q: Reset cleaning light (AOS U650, AOS 7135, AOS 7142, AOS 7144, AOS 7147)
A: The cleaning light does not automatically reset. Hold down the power button (button A in instruction manual) until the light stops flashing. The light automatically comes on approximately 14 days after plugging in the unit.

Try wiping off the cliff sensors, and cleaning the drive wheels. Download the user guide, if you don't already have one.

Grease Filter Saturation LED The speed 2 LED in Figure 1 in is marked with an F. This LED will flash to remind you when the grease filter needs to be cleaned after 40 hours use. Follow the instructions for cleaning filters in thisFollow the instructions for cleaning filters in this booklet. Once the grease filters have been cleaned, reset the display by pressing button A for

I read on another site to hold the power button down for 5 seconds. Dont know what the blue light is but this stopped it from flashing!

bang the side of the starter with a hammer (dead blow) and hold the start button. sounds like the starter solenoid is frozen. if not check the relay, and the switch, you can check the switch by doing a continuity test on it. good luck ill check back...

did try kenmore website
sears has a great place for trouble shooting

The light flashes after a certain amount of run time. It is a reminder to check the filter to see if it needs cleaning. Once you have checked/cleaned the filter and reinstalled it, press the filter button for 5 seconds and the light should go out.

try holding ice type and child lock together for 3 seconds that worked on mine