car will start with a bad alternator as long as the battery has power. It will also run a good amount of time if it is the 4af as there are many things running off the battery. Check all 4 wires for spark. Sometimes one will work but the others may not be strong enough anymore, been there before :|.
They may look fine and there might be enough fuel but that's not what retiredat44 means.
Hold each spark plug wire near (within 1/4") the valve cover and crank the engine over. Make sure there is a spark that jumps from the wire to the valve cover. That will make sure you are getting spark.
For fuel, you can just undo a fuel line and crank the engine and make sure gas come out.
If it's cranking over strongly, it's not the alternator. You can make sure of this by trying to jumpstart the car.
Besides a broken timing belt, it could also be a problem with the distributor.