Hi, I don't think Crystalfontz sells any displays that use the ili9341, so I can only offer general advice.
1) Find the correct datasheet for the display you have and ensure the pins are correctly connected to the BBB.
2) Check that you are following the initialization sequence outlined in the ili9341 datasheet. Some display datasheets will have the initialization sequence in the datasheet, some companies (like Crystalfontz) will publish demo code that includes the initialization sequence.
3) If you're still having trouble, it's time to use a multimeter or oscilloscope to check that pins are being pulled high and low as expected.