2011 GMC Yukon starter issue

[Seafarer]

Battery is fully charged. Engine won't crank. All electrics in the car work properly, but when I turn the key everything goes out for about 30 seconds and then resets, but starter will not crank.

[Jsdirt]

I would load test the battery. It can be showing 12.6v, but not have enough amperage to crank. When you let off the key, the battery recovers and has enough amperage to power computers and lights. That's my theory anyway. Easy, quick test.