Does a bad battery cause my tractor to not turn over?

Battery fully charged ? ? ?

Could be the battery might need charging or the solenoid is bad but try the battery first

Sounds like the electronic fuel pump. Could have a bad starter or solenoid. If battery is good, could also be igniter box. Are you getting spark, if you are then probably not igniter.

Could be 3 things valve lash is one. Second is weak battery. Third could be bad brushes in starter depending on how many hours on unit i would start with load teating battery then check the valve lash then go to starter

Does it crank? There are a myriad of issues to check

Dead battery
Bad battery connections
Safety switches not all in right setting (like a PTO/mower deck turned on that needs to be off for starting, or a brake pedal not pressed, or a seat not sat on)
Bad solenoid
Bad fuse
Bad relay
Bad starter switch

More details can narrow it greatly. Have you tried jumping it? Do you get noise when you turn the key? Was it an all of a sudden problem, a growing intermittent one, have you tested the voltage of the battery or tried charging it? Etc.

You may want to try to find a battery with a stronger amperage rating. Even if the battery passes if it is borderline for starting it new it may not be strong enough even if it's still okay for it's battery type.

Other causes:
A worn starter can cause this issue. If a few of the coils shorted the starter will work but require much more current to do the job

A bad relay/solenoid to the starter that doesn't allow enough current to go through can cause this.

Valves out of adjustment... especially on some Briggs and Stratton engines, it's a known issue that if the valves need adjustment the motor can require a lot of energy to turn over and can cause constant hard starts.

starter cylinoid is bad i almost bet

follow the heavy wire from the starter to the solenoid.
Also this problem is caused by a loose/bad/corroded ground connection

im sure the switch is bad, trying to jump is a good way to find out if the starter is bad but of course wont start cause of no spark, alot of these have electronic magnetos

it sounds like the battery doesnt have enough crankinc amps. thats a pretty big engine and should have probably have atleast 250 cranking amps. its possible the starter is going bad also