The failure in the video memory means the mainboard needs to be replaced - the GPU and VRAM are part of the system board and not separately replaceable.

Could you provide a source to the error code from the memory test? (I couldn't find anything on the web). Also if replacing the motherboard is the only solution, could you link a site where i can get a new one?

Thanks for your assistance

Dell diagnostic code chart:

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This system is old enough it may not make sense to spend upward of $300-500 to replace the mainboard, but parts-people.com should have the parts.

EDIT: After performing an Extended Windows Memory Diagnostic (since the short one wasn't giving any errors), I have found out that one of the RAM sticks was causing the shutdowns. After removing it, my laptop doesn't randomly shutdown anymore, and I was able to perform an Extended System Test which still returns an error. I read it might be due to overclocking but I don't recall tweaking it myself (although I have a refurbished model so it might have been handed to me like that). I'm adding a screen of the core clock speed as well.

Any ideas?