[spaetzle]

You replaced all the ignition stuff, so by process of elimination I would guess it is a fuel problem -> more specifically the fuel pump. The fact you can start the car up and that it runs for a few minutes and then dies seems to fit the "heart not pumping enough blood" problem. When you turn your key to ON (not to START), the fuel pump is told to prime the fuel system (pressurize the fuel line). When it does this, it is forcing fuel into the fuel line, but no fuel is being let out to burn at the other end (in the engine). When your key goes to START, the engine starts trying to use that pressurized fuel, and since the pump had a head-start, the engine will run for a bit. When the engine's demand for fuel catches up with the pump's head-start, the pump will no longer be able to supply enough gas to the engine, causing it to die.
The above answer is the most probable. It could also be a faulty fuel-pump relay (EASILY replacable by ANYONE, and it only costs $30), but the odds of that almost nil.