Looks like the cpu is running...
Maybe inspect pcb between cpu and MCU+GPS connector.
You can try the following, but not sure about the stm32flash.exe binary. Never tried under windows.
Short the two pads inside the black rectangle on gps board near the MCU+GPS port.
Connect a serial adapter or CC/CC3D/REVO configured with ComUsbBridge at 57600 to the usb port, then attach the serial wire to the gps (MCU+GPS port) and quickly run the following command :
stm32flash.exe -w ef_gpsplatinum.bin -v -g 0x0 <portname>
Where <portname> is COM1 or something
If it fails, disconnect the gps from the serial wire and try again... need timing.