First thing to do is to get the fuel pressure checked with a mechanical gauge.
If low then then more than likely you have a bad fuel pump. Located in the fuel tank.
Also have a backpressure test performed on the CAT, it may be clogged and that may, indeed, be the problem.
You never want to run a car out of gas, the gasoline actually cools, or dissapates the heat from the pump, running without gas will cause the pump to overheat and fail.
Check around with mechanics in your area for the best price and gaurentee, I would avoid chains, and look for independent mechanics who are ASE certified.