It seems that there is a short circuit in your board or in the Edison. I have checked the schematic you attached and I would like to know which value the potentiometer is set. As I can see in your design, you are using the following configuration for the voltage regulator:
Using as R1 the 220 resistor that appears in your schematic you will get a minimum output voltage of 1.25V and a maximum of 6.93V, so the potentiometer should be set to 536.8Ω approx. in order to get a value of 4.3V for Vsys. Did you measure the value of Vsys? If it was above 4.5V the Edison module is probably damaged and it is causing the short circuit in your custom board.
If you have another expansion board like the Mini-Breakout Board or the Arduino Expansion Board you could mount your Edison in one of them and test it to be sure if it is damaged or not.