I've never heard of this problem, Its not the key, they key doesn't have a battery in it along side the chip, I have an unchipped key I use to open my doors as a spare if I ever lock keys in, I've never been able to start the car with it.
It sound like there's a blockage somewhere delaying the operation, it doesn't have to be a completely failed part but on its last leg. If I was in your position I really would lean heavily toward the fuel delivery system (fuel pump or fuel sending unit, possible fuel filter or a blockage in the fuel line near its connection area) my testing if it was me who's having this problem is I would take out the fuel filter and disconnect the fuel line just before reaching the fuel injectors, I then would shoot compressed air in the line from one end and see if I'm exiting with the same pressure on the other end.
It sound like there's a blockage somewhere delaying the operation, it doesn't have to be a completely failed part but on its last leg. If I was in your position I really would lean heavily toward the fuel delivery system (fuel pump or fuel sending unit, possible fuel filter or a blockage in the fuel line near its connection area) my testing if it was me who's having this problem is I would take out the fuel filter and disconnect the fuel line just before reaching the fuel injectors, I then would shoot compressed air in the line from one end and see if I'm exiting with the same pressure on the other end.