Originally Posted by ahicks
Is there a chance that a wire was inadvertently left off or put on the wrong terminal when the battery was replaced?
Most definitely, but most smaller wires that go to the corresponding positive or negative post of battery have that wire either taped to corresponding larger wire or wire will be too short to reach other connector post.
There's also, which I didn't mention, the Alternator. For some vehicles, if the alternator goes out, it won't let engine run. So get alternator tested for power output.
Also check battery (+ & -) cables around battery post connectors for ANY corrosion. This will prevent proper voltage getting to any solenoid/starter or from alternator from properly recharging battery. Just get some water and baking soda and wet cable/post thouroughly and liberally sprinkle on the baking soda and let it do it's work. Do this a few times until you don't see any acidic reactions.
As I said, you have your work cut out for you and ANYTHING that deals with engine running needs to be checked out thru process of elimination.
Make a list of what you mark off as to checking/cleaning/wires connected and loose wire screws tightened/ground wires cleaned and rust at ground cleaned off for better contact. Everything.