I can't believe there's an Aveo forum and I never found it before today!

I've got a 2005 Aveo LT that I've had since new. About 2 months ago it broke down, leaving us stranded for the first time, and I've had a string of problems ever since. I'll list this out in chronological order, because the timing has GOT to have something to do with it...

Thermostat housing snapped in half while the wife was driving to work. Managed to get a new (metal) one and replaced it in the parking lot. Coolant had blown ALL over the engine.

A week later the wife calls on her way to work again and said the car is making a really bad screeching sound. Oh great. She makes it to work, and a friend and I drive up to take a look at the car (she works the night shift...) We go to start the car and it won't catch. We had to try about 4 times to get it started. Once started it idled rough, engine light and HOLD light came on and were blinking. (engine code ended up being Random Cylinder Misfire) We stopped the engine, took a look at top of the spark plugs and it looked like the valve cover gasket had been leaking and the coolant blowing around and made oil get down into the spark plug wells. We pulled them all out, cleaned everything up as much as we could, put it back together and it started and ran just fine. Then I backed out of the parking space and heard the noise. The freaking brakes were shot! LOL what a coincidence...

The next day I replaced the brakes and valve cover gasket. I also did a more thorough cleanup of the spark plug boots and wells. Car was running great... with one caveat...

Ever since the thermostat housing broke, the car has been hard to start. Some days it's worse than others, but what happens is this. You hit the starter and the car barely turns over, then sounds like it's going to die. Sometimes it does and you have to retry. BUT - once the car has been running for around 1 minute, something "clicks" (not literally) and it instantly starts running smoothly. Once the engine has warmed up at all, when you turn the car off and restart it, it does NOT give you any trouble at all...starts right up. It should also be noted that there is some valve tapping that seems to coincide with the rough idle.

The only things I've done so far are to replace the spark plugs (didn't change anything) then later changed the wires (didn't change anything).

Now it's getting worse. The difficulty of startup is still random from day to day, but now it's idling rougher than usual all the time. I'm going to be replacing the timing belt in about a week and would really like some insight into what else I should be doing at the same time.

To me it seems like an electrical or sensor issue. What else would make it suddenly "click" and run normally?

Would GREATLY appreciate any advice! And if anyone wants a non-rambling, "abridged" version of this post, just let me know...