Laptop shuts down automatically after 30 minutes

At this point if there is no solution consider testing pc with a different Sandy bridge cpu (Intel 2nd gen cpu, i3,i5,i7 or pentium G630 or the like). Pentium is likely the cheapest test. $4 free shipping. If new cpu recovers your iGPU and pc no longer shuts down, it is evidence that i5-2400 is culprit. If new cpu makes no difference, it suggests issue lies in motherboard chipset. Meanwhile use HWmonitor to test cpu temp over 30 min and verify it does not overheat.