That symptiom sounds much more like the DIS or the computer going bad. Mine did very similiar things....hard starting - but stepping on the gas caused it to fire and after it warmed up ran fine. See if you can hear the fuel pump when you turn the key on to the on position (but dont try to crank the motor). you should hear it buzz (very faintly) for no more than 5 seconds and then cut off. If you hear it running for 10 to 30 seconds and then cut off, then your computer is going bad. This happened to me. And I would listen for the pump to cut off and then turn the key and it would fire up fine - turned out the computer was bad.
I did have bad coil packs that i replaced, it ran great for a few months, then started missing again - thought it was coil packs - put on a set known good spare coil packs i have, was not the problem. The tach started reading funny (like at idle was reading 2500 RPM and the engine was misfiring a bunch. Replaced the DIS and it ran great for 6 months. Then it started with the hard to start but eventually did - keeping my foot on the gas until it fired. Thats when i noticed the fuel pump running with key on no start for an extended period. found a nice computer in the junkyard - you could tell it was a new replacement one, plugged it in and been happy cruising since then. (I tried other things 1st, from thinking it was a clogged fuel filter (well it needed replacing), to a new fuel pressure regulator, and new fuel pump. None solved the problem until i replaced the computer. But I think your problem is either the DIS or the computer.
Hope this helps.