Hello,
Not sure I understood all well.
Your starter is engaging ? But can't spin the motor ? Other load (lights) working ?
About a battery, you should load it to test it. It's what a battery tester is doing. Reading the voltage can give you an information of state of charge, but can not determine the health (or condition) of the battery.
By the way, I always read "my battery was flat and I recharged it it is ok". No. No no. A lead acid that drop bellow 10.5V start irreversible sulfating, so it deteriorate - the only question is a few or a lot.
Lawn tractor guys, keep your battery charged during winter