Crispin:
The solar panels do not share ground with the supply.
There is your problem. Without a reference the voltage can be anything. But it should not exceed Vcc, without reference, how can you be sure? Give them a shared GND 
And to be sure, also check the voltage to after the divider with a DMM.
And note, the ADC might not be very happy it there is a voltage on it's input (from PV) but no Vcc.