Also a schematic would be of great help.
Either way, if it worked on a breadboard, but doesn´t work on a six! layer board with two ground planes then something is amiss, like a bad solder joint or a component in a wrong place. Or something in the schematic that didn´t show up on the breadboard, like the added stray capacitance of the ground plane.
The board looks so simple that you should be able to comfortably do it in just two layers without any issues, I have no idea why you went for six on the first try, it must have been hugely expensive.