Over the winter we had a lot of snow in my area and my crown vic sat while I drove my truck. After the winter had ended I attempted to start the car but it wouldn't start. I had treated the gas and replaced the battery but the car just turns over. After spraying some starting fluid, the car ran briefly but died once the starting fluid had depleted. I checked the fuel rail and it is getting fuel at the engine but still won't run. Could the gas have gone bad?

Check your fuel pressure with a gauge. I understand you said you are getting fuel at the rail, BUT you also need to correct pressure.

Clogged fuel filter?

As far as bad gas, Gas has to be REALLY REALLY bad for the car not to even run. Water pockets could be a cause of REALLY bad gas. When you check your pressure, take a sample from the fuel pressure drain on the gauge and see how it smells.