Is the PIC power supplied by a stable voltage regulator, fitted with suitable bypass capacitors? Have you checked the impedance of your clamping circuit feeding the PIC?
It seems the signal impedance is very high in your case, otherwise it would not be affected by the small current of a LED. A buffer between the signal and the PIC pin is required if the impedance is higher than 2.5Kohm as recommended by the PIC datasheet.
You would need to post the schematic of the clamping circuit, A/D input to PIC and the PIC power supply arrangement for additional comments.