The problem is much more likely to be something preventing the engine from continuing to run *after* it starts:
* Fuel delivery: Clogged fuel filter, faulty fuel pump, problems with the fuel injectors. The car might be getting a brief burst of fuel then nothing.
* Ignition system: Faulty ignition coil, distributor cap/rotor (if it has one), ignition wires, or crankshaft position sensor (this is a common culprit on older cars). It might be briefly sparking then failing.
* Air intake: A severely clogged air filter could starve the engine of air. Less likely, but possible.
* Computer issues: A problem with the engine control module (ECM) or other sensors could cause a brief run then shutdown. This is less likely than the other options.
You need a proper diagnostic. A mechanic should be able to test these systems to pinpoint the problem. Just replacing parts randomly is a very expensive way to fix the car. Explain the symptom clearly ("runs for one second then dies") to the mechanic.