It uses U-boot as the bootloader which is meant to output to the UART before it reads the SD card.
I will check the power supply with an oscilloscope tomorrow but I doubt that's the problem since I have tried 3 different ones.
Also the board looks completely normal to me, although it would be easy to miss a bad solder joint or something. On my version of the Parallella there actually is no reset switch (SW2 is unpopulated) because it wouldn't fit under the heatsink, but I tried manually shorting SW2 with no effect.