Are they resetting on power up? Reset button make them reset?
Is the oscillator oscillating?
What is the difference in power supply current between working and non working? Higher in non working might indicate short, solder bridge, too much flux.
JTAG connection?
Boot loaded programmed in?
On the PDF of the PocketBeagle-VDD power plane, only P1.14 and P2.23 appear to be connected, I could have missed the other connections. Again on the GND plane, only P1 and P2 connected. I guess the vias do not have thermals.