My 02 Civic has a strange problem. Whenever I start the car the gas gauge, speedometer, and tachometer indicators flap up and down for a few seconds and the trip odometers reset to zero. This started intermittently and now it happens every time. When the key is in the accessory mode, everything is fine, but when I turn the key all the way, this happens. Otherwise the car runs perfectly. Any ideas about what this might be?
It appears that you definitely have an electrical/electronic problem.
Usually, counters and gauges are controlled by digital electronic logic circuits.
It could be some shorting in one of your wires causing a voltage level to change when you turn the ignition. This could reset your odometer. Specifically, I need to look this up for your vehicle.
It is probably controlled by an electronic module and its circuit wires.
I will follow-up in a day or so with a more definitive answer for your vehicle.
Have your battery tested. A weak battery can cause issues like those.