Chosen Solution

I have 820-00165 which shut it self off after 5-15 minutes: I thing its Processor short to ground as C1031 shorted to ground 29 Ohms. need expert view please.

I go with battery first. A weak battery can show a full charge, but drop to 0 quickly. Then monitor temps. If CPU temp is over limit, it will shut down.

29 ohms to ground is not considered a short on the Vcore (CPU) rail. Test with a known good magsafe (original is preferred) power adapter. It is ok to remove the battery and test with the external power adapter only. Does the logic board power up and remain to be powered with the external adapter ?