Wont start as if battery is weak but battery is good.

Does the car push-start (or actually the engine crank turning)? If yes then it has to be a battery or starter solenoid/starter motor problem. In some cases it can be the power cable to the starter motor. Check the terminal connections to be clean, good and solid. First of all though check the voltage drop at your battery when the key turns to start. If the voltage drops under 10V then your battery is weak and you should try either jump starting or put another known good battery and test.

Batteries can read fine, voltage-wise, but they can still be way down on current. Check the voltage while you are trying to crank the starter. If it drops below 8 volts, then the battery is weak or the starter is drawing too much current. If the battery is more than three years old, suspect it first.

the alternator lamp will not go out until the engine runs..
the alt converts engine horse power to electric power,
no engine, no alt.
so that means the engine will not start, or better it wont crank
subzero C or Subzero F.,, -10F or -10C, vastly different temps.
???????
no crank, then jumper cable crank it with donor car running.
crank now,?
yes , then battery is bad,weak or just discharged.
no, then starter bad, or key line bad.
hot wire starter solenoid. cranks now, is bad key line
if not, bad starter.

did you wiggle the shifter at crank.
did you wiggle key. extra.
did you try crankiing in neutral using fresh start contacts.>... yah.

you mean it wont crank, it must crank to start.
1: bad starter system
2: weak battery even a new battery can be weak.
if you dont charge it first.
or if it starts ok then wont later, that means cars charge system failure.

can you jump start engine? with jumper cables.
that be a big clue there, proving starter works but battery was weak.
if the battery is fully charged.
you can hot wire the starter solenoid, (tiny terminal)
if car cranks now, the key start wire is failing.
A/T or M/T tranny? both use different path here....??????

if you cant hot wire it, then that means the stater is bad
the cables bad or the battery is not really connected.
or possible the engine is seized, can you hand turn over the engine at the front crank bolt (CW , facing rear, in neutral)
if not motor is seized.
some times even the starter and rig gear can be seized.
the starter can be bench tested. too.
http://www.fixkick.com/nocrank.html

turn on the headlights and try to crank the engine; if the lights dim out while you try to crank, then the starter is ok but the battery is too weak. just turning on the lights does not mean that the battery has enough juice to crank the engine; a starter pulls a lot more than lights. If the headlights do not dim out and it still won't crank, then the starter or a connection to the starter is your problem.

If it wont crank then there are 3 possible problems: ignition, battery or starter, If you have a weak crank then it narrows it down to battery or starter.

To begin with, turning over means different things to different people.
Does the engine crank but not start, or not crank at all ?
If it cranks but does not start, Honda cars are known to have weak fuel pump relays which would need to be tested.

check starter check for low battrey volltage

If it doesn't turn over it may be your starter going. or a weak battery. start with that first, insufficient fuel pressure won't prevent you car from cranking, but weak battery or bad starter will. If you can jump it and it starts its probably the battery if it doesn't crank then its probably the starter. Good luck

sounds like the battery may have a dead cell. When they charged it at autozone did they test it to make sure it was still good? most times if you run an old battery completely dead it will not recharge all the cells.