I'd recommend taking a good look at your battery harness connectors. Make for certain that the wires are snug within the connectors and will not wiggle about inside them. Check for signs of corrosion and remove it from contact surfaces if it exists.
In the case of a side terminal specific application, these connections are notorious for having poor connectivity when they get older. Corrosion can build up inside the housings and insulate the bolt from the contact ring that it goes though. I have had these go bad on both a buick lesabre and pontiac montana that we have previously owned. The lights, door dinger, radio, ect may al work, but when attempting to crank the car over you often will be met with a single click before everything dies until you release the key.
The buick more or less kept us from starting the car, the montana i've had it kill the engine while driving it. (it was a bad winter and I 180'd it when taking a corner at 25mph. The engine died and I couldn't restart it until I tugged the cable 90 degrees to make contact and get to work. Had i never owned that buick and knew the batteries were a pita, i would have never guessed. I didn't have tools on me at the time. More than once had I thought my buick had another issue, i'd check the terminals and think that they were fine. They didn't wiggle or anything, but at the suggestion of my father, i still tried to make sure with the wrench, and what do you know, it turned over.
if this is the case, you can usually give the terminals a little extra snug with a wrench and it can temporarily alleviate the problem. This crushes the bolt down onto the corroded ring inside it and offers the extra contact that it needs. (Be careful not to go too far, you dont want to strip the battery threads! We just want it firmly snug!) The connector itself should be replaced if this is the problem. Whether you replace with the OEM style or go top mount, that's up to you.
You might also be able to hook a battery jumper up to the backside of the connector in an effort to help it bypass the battery in the circuit to see if that lets it start.