96 Intrigue won't start

Seems like it's got good power, tried jumpin it a few times and still only clicks.
Clicking is def from the starter. Pulled it out and took it to AutoZone--it passed the bench test. Check connections @ the battery and @ the starter-seemed fine; clean and tight.

Where else should I check for a bad connection?

The "Service Engine Soon" light has been on for about a week. Any relevance? I don't really wanna pull the alternator off if I can avoid it; any way to test while on? Why would that keep it from starting anyway?

It started not two minutes before it didn't start again (I started, backed up, turned it off, ran inside for something, tried to start again and "Click".)

Any help'd be great.

Well these cars are known for ignition switch issues. Theres usually no clicking involved though. Usually a lack of clicking.

The alternator should not keep the car from starting, I've heard that a lot and I personally think its an old wives tale. It could keep it from starting in a roundabout way by making the battery run dead, but with a healthy battery, or jumper cables, I cant wrap my head around an alternator causing a vehicle not to start.

I would pull the code if you can, might give you a hint, might be nothing...but the car does not need to be running to pull the code. If you dont have one, some places will let you borrow a code reader, or they are pretty cheap to buy. I bought mine off Ebay for 20 bucks, you can get them in store at places like Harbor Freight for 60-70 bucks these days.

The only other thing that comes to mind is that your positive cable might be damaged or severely corroded internally. So even if the connections on both ends are clean, tight, and secure, the cable in the middle could be junked.

Or it could be that you just need a new starter, bench test might have been a fluke.

First thing is to get the code read for the "Service Engine soon" light. it could be related, it might not. Just about all the issues with the Intrigue have been addressed on this forum. With the code and the symptoms you described, someone can help.

Second, how old is the battery? The last two batteries i had to replace would not start even with a jump. I didn't read in your post that you had the battery checked, just the connections.