FPGA simulates well and passes timing check but fails in PCB
As an answer to your question "What do you do next", here's some random things you should consider and measure:

Does it get programmed OK? Do you use some JTAG cable to connect to it? Does it identify itself correctly with the JTAG cable and programming software? Or do you use some EEPROM/FLASH to load the configuration at startup? Do you program the bitfile to the EEPROM/FLASH using the FPGA vendor's tools or with some other tools? Does the EEPROM/FLASH get programmed ok? Does the FPGA signal DONE after boot / after loading the configuration (Xilinx)? Does it use a reasonable amount of current? Does the current change when the configuration is loaded? 

With all digital circuits, everything comes to three basics: Power, Clock and Reset. Try to confirm these, one by one. Try to generate and load a configuration that does very basic things, such as pulling some output high, another low. If you have some buttons/LEDs on board, try to route some button signal directly to a LED signal. Anything that doesn't require a clock. Then add a binary counter from the clock source to some outputs. Measure that you get some outputs toggling up/down with the clock.