I have a 14.5 hp briggs&stratton engine that just barely turns over,battery good what could it be?

If it is an OHV (over head valve) motor the valve lash probably needs setting. There are many videos on you tube that shows you how to do this. Just Yahoo or Google "setting over head valves" and find one you like.

When you take the plug out, you have no compression, that is why it is turning normal. This could be the starter or the solenoid going bad. Take the starter off. If you have a battery charger hook it up to the starter and turn the charger on. See if the starter is spinning good. Are you can take it off and take it to Auto zone or a parts house that can check the output. Like I said this may be the problem,or the solenoid. Take them both to the parts house.

If a starter is dragging under compression it is losing voltage. Also make sure the battery is fully charged. This is the first place to start. Also could be the valve adjustment, but if you have never done this you could very easily screw it up. B&S motors are not junk,they are good motors and well worth the time to fix.

Start with the simple problems. Clean and tighten all of the electrical connections. The negative lead gets loose on the engine frame quite often. Then try bypassing the starter solenoid with a jumper wire, if it still cranks slow after that, then the starter motor or the engine is the problem. Remove the starter and have it checked at a parts store. I'll bet on loose or dirty connections first. They are the cheapest and easiest to fix, then the solenoid. Have fun.

typical of bad connections or having the cylinder full of gas/oil from the carb flooding. check the oil to see if its overfull/smelling of gas. tighten all connections. you sure the batt is good? how do you know? it may be weak/under charged even if it reads 12.6 under no load.

edit: oh yea if its OHV check the valve lash for sure. comp release won't work if its too loose.

check the key way on the flywheel,

did you hit something last time you was using it ?

sounds like it,s out of time, [the key way keeps it in time]

or it was ran with out oil,

99% of B & S stuff is garbage. Toss it. I have owned several of them and hated every one.