Remove the PIC from the picture.
1. Measure the voltage of each cell.
2. Measure the voltage of the combined cells.
3. Connect diode and measure the combined voltage again with diode.
4. Attach a resistive load which will draw equal amounts of current expected from the PIC.
5. If you have a scope, monitory any ripples.
6. If resistive load pulls desired current and battery supply maintains proper voltage and ripple, then you can now scratch the new supply off the list of faults.
Swap PIC in question with another known good.
Get back to me when these are done.