Q: Macbook Pro Issues

Thats entirely a bad idea to buy this module of MacBook which is made in 2010

i assume your having the Nvidia 330M and its proofed that theres a defect which is already made during the manufacturing process which is causing the discrete graphic card broke down after years

and the 2011-2013(mostly 2011 non-retina) dual graphics card MacBook Pros are suffering almost the exactly same issue with their AMD 6750/70 NV650M cards.

unfortunately the quality program for the 2011-2013 Macbook pro still seems ongoing, but for your MacBook, the quality program already ended.

Sorry for let you hearing that, you might try to give the machine back to where you got it from before by telling them the reason, otherwise you need to pay the expensive logic board repair about 500 bucks(which is not worth to pay that price for a 2010 Mac), and not sure Apple will replace your board with the 'defect-fix' version or just using a exactly same board which is going to break eventually after about 2years.

And when you decide to getting a second-hand machine, always check 'bout all the details before you getting that

JasonNvm

yes, i entirely knows wacha saying, theres a RUMOR (not officially proofed by Apple), that saying the cause of the problem is Apple trying to use some type of environment friendly lead-free material on their board while doing 'BGA work' (welding on the discrete graphic core) for the defected MacBooks and Apple screwed it up becuz the material will slightly liquify or 'unweld' when its got heating up by the graphic core, during this dramatic process if the graphic core got slightly detach from the board then of course the entire system will immediately glitch out (if discrete core has been active at that point, or your trying to boot which is require the discrete core to pass the booting process)

but you letting your computer sit a while after successfully boot also help the material re-attach somehow, so it might helps for SHORT PEROID OF TIME.

you may try to use gfxcardstatus to force your computer lock onto intel graphics card (lower performance but also lower power use), that could prevent the active of your defected discrete card. and this considered to be the only solution other than hardware repair, and you do need to realized you do need to remember that try not to shut your mac down completely, just sleep it. cuz if the card fails during the booting process, you will not having a chance  to re-lock your computer onto intel graphic if you can't get into the system

JasonNvm

Check to see if there is a kernel panic report in your Library.  If so log and post it per these instructions:

https://support.apple.com/en-us/HT201753

Ciao.