When you run out of gas, you risk:
* Air in the fuel lines: The fuel pump needs fuel to prime itself. Running dry can leave air in the lines, preventing fuel from reaching the engine. This is the most likely culprit.
* Fuel pump damage: Some fuel pumps rely on the fuel itself for cooling. Running dry can overheat and damage the pump.
* Damage to the fuel injectors: Similar to the fuel pump, the injectors could have been damaged from running dry.
What to check first:
1. Refill the tank: This is the obvious first step.
2. Listen for the fuel pump: Turn the ignition key to the "on" position (don't crank the engine). You should hear a brief whirring sound from the fuel pump (usually located in the tank). If you don't hear it, the pump may be dead or the fuel pump relay may have failed.
3. Check fuel pressure: This requires a fuel pressure gauge. Low or no pressure indicates a problem with the pump, filter, or lines.
4. Check for spark: Verify that you are getting spark at the plugs. A no-spark situation is a much more common starting issue than a fuel filter.
The Fuel Filter: A severely clogged fuel filter *could* contribute to starting problems, but it's more likely to cause poor performance and stalling *before* the car runs completely out of gas. If the other potential issues are ruled out, then the fuel filter becomes a more likely suspect. However, it's relatively inexpensive and easy to replace, so it might be worth changing it even if it's not the primary problem.
In short, running out of gas creates several potential problems, and the fuel filter is lower down on the list of likely causes. Address the potential for air in the lines and a faulty fuel pump first.