I'm shocked! There's indeed no ground plane at all. (Although Pathipati told us to have implemented one!) So, if there's any interference hitting the board it can take a bath in the wildly routed ground traces providing a universe of wild resonances. Such a design is totally unsuited! And it's not a question of adding some decoupling capacitors to get it properly to work...

Pathipati, your board NEEDS a solid ground plane. By solid I mean something which covers the WHOLE board and isn't interrupted by any gap! From the many vias and trace crossings that can be seen from the photo this demands a four layer board!

Try to locate all inputs/outputs in such a way, that they will enter/leave the board at only ONE edge. This prevents interference hitting one cable from running across the whole board and introducing ground noise.

Kai