If the FI unit is at fault, the most probable cause is a defective Cranking Signal Valve. The most common failure of these is for them to fail open which will let the engine start, but it will run excessively rich. However, I've also seen them fail closed and extremely difficult cold starting is the result.
Try spraying some starting fluid in the mouth of the Air Meter.
If the engine starts and continues running, the CSV is likely at fault.
If the engine starts and dies, something else is wrong with the FI.
If it doesn't even fire, look for an ignition problem.
Good luck.
Jim