I have a 10 yr old Trane XE1100 AC (no heat) which ices up at random unpredictable times. It has been doing this for several months. Cooling is good.

I installed a new contactor recently because it showed black deposits at the contacts.
The unit was recharged about a month ago, last time was 2 years ago.
The evaporator and condenser coils have been cleaned.
The filter is cleaned regularly.
When I catch it icing up at the condensing unit outside with the pump running, I find the blower fan (air handler) has turned off.
When the t'stat fan switch is put to the on position nothing happens.
When the system is switched to off, the pump stops immediately.
If the fan switch is then changed to on position, the fan starts right up.
After the ice melts, the unit runs normally again. It could happen again the same day, or not for weeks.

I hate to just change out parts, hoping that I accidentally find the right one.
I'm a decent handyman, but know very little about AC systems. My only guesses are the thermostat or the fan relay.
Any help would be much appreciated. This is driving me crazy.

I am a car AC man, when it freezes up it is shutoff by the coil thermostat to prevent the coils from freezing so that the fan can blow through the coils, after all, it is a heat transfer device and the ice will keep if from doing its job and the expanding ice may very well damage the coils. Home AC's are serviced using superheat and an accurate temperature measuring device, I am not 100% so ask you technician about this. Hope this rattles a few marbles and gives you some food for thought.