Air conditioner locating c wire on old unit
This wiring could do with a bit of cleaning up

As you pointed out that Cable 3 (the rightmost cable in the photo) at the air handler goes nowhere, we can take it out of the circuit entirely by nutting the red wire from the air handler to the red wire from Cable 1 instead of the red wire from Cable 3.  (This means that the blue wire from Cable 3 is no longer nutted to the red wire from Cable 1, too.)

Once that's done, finding C isn't so hard after all

Now that we have that useless cable removed from the picture, we can find C rather readily, given that we know how the outdoor unit is wired; in particular, green and blue in the cable to the outdoor unit are connected to the contactor, with the other wires left unused.  Since we know that the blue wire in the cable to the outdoor unit is connected to the blue wire in the cable from the thermostat, we can safely presume that this blue wire is the Y wire, leaving the green wire to connect to C on the air handler.

Since we have a good indication that brown is C as well from the scant documentation available for your make of air handlers, we can safely assume that the junction between the thick brown wire and the thin green wire is where you need to connect the white wire in your thermostat cable to use that white wire as C.