I'm having trouble with this part of my circuit. I have this crystal connected, but I see only a 3.3V DC signal on Pin 1 and 3 of the Crystal, and a 0V signal on Pin 2 and 4 of the crystal. I'm wondering two things:
Your schematic symbol is wrong- it looks like the GND pins are shorting the oscillator input and output leads to ground internally, and I doubt your crystal is made that way.
Here is a typical 4 lead SMD crystal:
Check your crystal's load capacitance parameter- the values you show might be okay for an 8pF load spec, but not for an 18pF. (Should be about double the load capacitance number, minus a few pF).
Check also that you have Rref 12K 1% to ground from the REF pin of the FT2232H, and that the 1.8V regulator output VREGOUT is actually close to 1.8V and connected properly to VREGIN assuming you're using the usual circuit.
Usually an oscilloscope probe (even a x10, but definitely a x1) will cause the oscillator to stop when connected to OSCI, though you may be able to see a waveform with a x10 probe on OSCO. Crystals do not have polarity.