I'm the furthest thing from a mechanic and was hoping someone might be able to help me with a few questions.

First, I haven't driven my '98 ZX2 for over three years and am trying to get it running again. The last time I started it was a year ago and after that, the battery completely died. I just replaced the battery this evening and though it's trying to start, the engine won't turn over. Could this be because it hasn't been started for a long time? Should I keep trying or will that do more damage than good? What other things might cause this to happen?

Finally, when I was replacing the battery I noticed something that I did not recognize - not really a big surprise since I'm not familiar with engines. I was hoping someone might be able to tell me what this is from a picture and to what it's supposed to connect.



Thanks so much for any help you can offer!

 

It's hard to tell where in the engine compartment you are in your picture. So I looked for another picture of a ZX2 engine compartment:

In this picture is a connector to the air filter body. It is the MAF sensor harness.
If the MAF sensor is disconnected it definitely will have trouble starting.
Back towards the firewall you will find a connector tot eh wiper motor. Do your wipers work?
And a connector the the throttle body position sensor. That could cause starting trouble as well.
If the connector is near the washer bottle it could be the connector to the air conditioning. That should not cause starting trouble

Here we need to clarify something. I suppose when you turn the key it goes " oi-oi- oi" but not "vroom!" That means it does turn over but it does not fire up. Your starter is fine but you have either no spark, no fuel or no compression. Spark and fuel need to come at a certain time and fuel must be injected in the correct amount.

When a car stands around for a long time the gasoline may go stale and cause cruddy precipitate in the tank, fuel lines, injectors. It could clog something, meaning you have not enough fuel for it to fire up.

So put in fresh gas, maybe you can get the old gas out first. Find out what this thing connects to and give it a try again.

 

That looks like the "stuff" that attaches to the negative ground cable at the battery. I changed my negative ground to the battery and ended up attaching that mess to a ground point on the frame to get it away from the battery.

When my 99 ZX2 wouldn't fire up, it ended up being the crank position sensor was busted. When I replaced it it fired right up after sitting for about a year. Bad thing was that the new sensor was too long and busted the corner off of it as well. I had to replace it a second time and use a couple of washers to space it back so it wouldn't get hit by the flywheel.

 

If the car ran at the time it was parked and no one touched anything under the hood I wouldn't be concerned with extra plugs at this time.
I agree with the suggestions offered by bluewind.