You really didn't follow through on that battery test properly. After charging, (via charger or driving the car), disconnect the battery and let it sit for at least two hours, three would be better. One hour is not enough. Then test it with a VOM, not by hooking it up, starting the car and looking at the voltage in the cluster. But the 12.53 volts you got seems a little low, but without the proper test, there's no way to be sure. The minute you start the car, your alternator bumps the surface charge up on the battery, quickly overriding any juice you used starting the car. The problem is that the surface charge will give you a false high reading. A good battery tester will not be fooled by the surface charge. But if all you've got is a VOM, you need to deplete that surface charge fully before testing.

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2014 BMW 328i Xdrive
2011 BMW 335i M-Sport
2008 BMW X5 4.8i Sport
2000 BMW 528i 5sp