Failed illinois emission test for no communication. Car will communicate with our snap-on solus pro. Any ideas?

Yes.
The OBD connector for the scanner is powered by the same circuit as the cig lighter. If the fuse is blown, the testing facility can not access the computer on the car.

Check your fuses and replace any that are blown. Usually the cigarette lighter fuse also powers the DLC (data link connector) with this fuse blown the scan tools can not communicate with the OBD2 system.

Start from scratch. Remove key and retry it.

You only have a service bulletins for the steering angle that gives code P0778 and 01044 . Now if the vehicle doesnt communicate and it communicate with regular scan tool then its the analyzer fault and you can go to a referee. When VW doesnt communicate its either due to the aftermarket radio that over voltage the diagnostic link.Another possibility is the cigarette lighter which power pin 16 on the diagnostic terminal is non op.For the abs that has nothing for the emission test

The ABS controller has failed (the two lights and the beeps are the telltale). Replace it or have it rebuilt at www.modulemaster.com.

First the fault codes,
U110C is No Fuel Level Bus Message
U0155 is No Cluster Bus Message.
Unfortunatly you have to be able to communicate with the instrument cluster with your scanner to diagnoise and I do not think an aftermarket scanner can do this.

Your emission sensors seem to be just a 'spec' out of normal (I would not call them defective!), but it could also be tainted fuel. Just to pass test I would buy the gas treatment at your local auto parts specifically for emission testing. Ask them at the counter. It will get you passed.

U0121 Communication error to ABS HU/CM

Hey check wheel bearings. I was told that this is a sign that they are going bad. or there is a wire runs to the back of the wheel that may short out.

check your exhaust valv and as for not being able to connect to OBD system, check all of your fuses.