Chosen Solution

i ran an Apple Hardware Test because The MacBook turns off without the magsafeThe battery status LEDs do not indicate anythingI have tried 2 batteries but the problem still occurred

4SNS/1/C0000008: TN1D - MCP89U - Internal of the chip die. This is the combined NVIDIA GPU/PCH chip.

Here’s a map view of the thermal sensors

Sadly, this is not really repairable as the chip will need to be replaced and unless you have the correct tools its just not possible. Time for a new logic board MacBook Pro 13" Unibody Mid 2010 Logic Board Replacement and here are your choices: MacBook Pro 13" Unibody (Mid 2010) 2.4 GHz Logic BoardMacBook Pro 13" Unibody (Mid 2010) 2.66 GHz Logic Board