Hi,
In your original code ( TRISA=%00110000 ) leaves PortA.2 as an output which is wrong.
In your post you contiune to say TRISA=%00110010, to set LATA.2 as input which again, as mark_s points out, is wrong, the above will STILL leave PortA.2 as an OUTPUT.

Your setting of ANSELA in the code is commented out which doesn't really have any effect on the ADC input since it defaults to analog but it WILL have an effect on the pins you want to use as digital.

The ADC DOES put a load on the node when it samples the input that's where the max input impedance comes from. Too high impedance and too short sampling time makes the voltage at the node droop when it's sampled.

/Henrik.