A honda shouldn't require much amperage to start. Battery output vs life is a bell curve, and it sounds like you're on the steeply dying corner of said curve.
A stupid test would be to leave your high beams on for 30 minutes then try to start it. If it doesn't, your battery was bad. Most car batteries have 60 plus amp-hours; high beams take around 11 amps, so this would be ~10% of a new battery's capacity-- but potentially most of a bad one's.
I don't know why your town doesn't have a midtronics tester-- every garage should have one.
Honda puts the smallest posable battery in there vehicles. If his 2005 Accord is a 6 cylinder it most likely has a group 35 or 34 maybe a 24F (all three are about the same capacity), if it is a 4 cylinder it most likely has a 51R. And of course most manufacturers make several different levels of each of those batteries.
A top tier 35 would have 100 minutes of reserve capacity. That is 1.66 hours. 1.66 X 25 Amps is 41.6 Amp-hours.
A low tier 51R would have 75 minutes ( or even less ) of reserve capacity. That is 1.25 hours. 1.25 X 25 Amps is 31.25 Amp-hours.
So we can expect a new battery in an 2005 Accord to have somewhere between 41.6 to 31.25 Amper hours of capacity.
If it was one of the smaller ones and only charged to 80 % that would mean it started out with only 25 Amp-hours.
If the headlights draws 11 Amps and he left them on for 1/2 a hour that would drain 0.5 X 11 = 5.5 Amp-hours. That is a little more than 20 percent if it is one of the smaller group 51R batteries. Still, after that drain, if the battery was in good condition, it should be able to start.
I would agree that leaving the engine off, and the headlights on for 1/2 a hour, and then turn off the headlights and try to start it as a test of the battery. If it starts the battery is most likely still good. If it does not start then, replace it.
