engine would not start...not like a battery problem, just wouldn't turn over

Find an independent Honda specialist, if the dealer isn't motivated enough to find it. Maybe the car started OK and they just passed on it. I suspect the fuel pump but the way to find out anything is to get it diagnosed by a competent and motivated technician, like an independent. Here's a directory link for you: https://repairpal.com/honda-repair-in-columbia-south-carolina

When you say just won't turn over. Do you mean the engine won't even spin over that sounds like dirty cables,loose starter wire or bad starter. But if the motors spinning and it soulds like its going to crank but won't that could be a clogged fuel filter or bad fuel pump.