I would focus on the A/D reference circuitry in the block diagram:
There are three sources of reference: AVCC, INTERNAL 1.1V REFERENCE and AREF, with two switching options in the ADMUX register - a multiplexer and a switch to AREF.
So I would first look closely at your code to see if the multiplexer and switch were set up absolutely identically (configuration-wise AND timing-wise) for ADC2 and ADC3.
If you find that there are absolutely no differences in the code for the mux and switch setup, one could easily speculate that the IC design does not ensure identical behavior (especially timing-wise) for all A/D inputs. The design software typically optimizes for size, speed, crosstalk and other parameters, but not necessarily perfectly identical sequencing. Under normal operation, a small difference in sequencing may not matter, but with AVCC unconnected the timing differences could lead to different behavior.
A third possibility is that your specific ATMega was damaged by whatever caused the inductor damage (e.g. maybe the board was bent, dropped or badly soldered). This could be verified by getting a second board, temporarily removing the 10uH inductor and checking for similar behavior, or, if you have the right soldering equipment, simply replacing the existing ATMega with a new one.
