@falloutames I would guess that the Nvidia card is unusable, whether through age or some other cause. The fact that the dxdiag doesn't even detect it enough to say there's a problem with the card is telling, although that could in theory be caused by a bad driver.
When Sims 4 launches, the system likely calls the Nvidia driver, but the driver is useless without the card, and it throws errors that are serious enough for Windows to initiate an emergency shutdown. Remove the driver, and the system defaults to the still working Intel graphics chip and its driver.
I don't know whether the Nvidia card could be repaired at all—that would depend on the issue and how this particular laptop was built—but I would guess that it would be much more expensive than it's worth. If you got a cheap quote, or maybe even if you didn't, you'd probably just be receiving someone else's used laptop with the same (or close enough) hardware, perhaps with your hard drive switched out. That doesn't really seem worth the price.