I\'d have them do a compression test - pretty simple to do and can give you more information to work with. You can swap coil packs from plug to plug to rule out a bad coil over plug unit, if it stays with that particular cylinder. Some possible culprits:
- a bent or stuck valve
- broken or stuck piston rings
- leaky valve seal
- dead piston (cracked or damaged piston head)
- heavily scored or out-of-round cylinder
- dead or sticking injector
- damaged camshaft (unlikey)
Could also be an issue with the induction system (airbox, intake manifold, throttle body, etc.), fuel system (fuel pump, fuel filter, pressure regulator - all inside the tank, fuel log under the hood), ignition system (coil packs, plugs properly gapped with appropriate plugs, good chassis grounds, crankshaft and camshaft position sensors are working), or engine computer issue (they can suddenly die with no warning).
Also - after swapping out coil packs, you should have reset the ECM so that it relearns fuel trims and other engine parameters - good idea to do this with any part change as well. Easiest way to do this is to pull the negative battery cable off for a few minutes and step on the brakes to bleed off any residual charge. Of course, if you have an anti-theft radio or similar - make sure you have the code for them, or you\'ll end up with a paperweight.
I\'d also make sure there is no other underlying issues that will compound the symptoms. Double check the vacuum lines for leaks and cracks, even missing vacuum lines - check the PCV valve. Check the induction system to any leaks or cracks - a leak downstream of the airbox or around the intake manifold (some Corolla/Matrix had a cracked intake manifold or bad intake manifold gasket), or leaky throttle body can cause an overly lean mix - as the ECM cannot see that extra air coming into the system. Check the MAF sensor and associated IAT sensor - generally not a serviceable part - many had very good luck cleaning it with throttle body solvent, alcohol, or brake cleaner. Same with the throttle body, make sure it is not gummed up with varnish or carbon deposits - a good scrubbing with throttlebody cleaner and an old toothbrush works wonders. Could also be a bad tank of gas - if there was any contamination in the gas (water, diesel, etc) it could look like oil fouling on the plug. Run a good quality fuel injector cleaner, like Redline or Chevron, in the tank and see if that changes anything.