2004 Mazda 3 bogging down
 

We just bought a 2004 Mazda 3 that wasnt running right, thinking it was a catalytic converter. It's hard to start, as in, I turn the key, it cranks a few times, will rev up, but then just die. After about 5 times, it starts and idles. But, when you press on the gas pedal, it bugs down real bad. If I press the pedal slowly, it accelerates normal. Last owner said the fuel pump, and I believe one coil pack was changed, as well as the battery. I removed the exhaust manifold, and no change. Almost seems like a fuel problem, but not sure. Does smell a little like too much fuel though. Any help would be greatly appreciated.