Video Card Error - At a loss

@libbyjb  Your dedicated graphics card is not showing up at all in your dxdiag.  I don't know whether it's dead, or the slot it sits in is dead, or the card or its power cable (if applicable) isn't seated properly, but the fact that Windows doesn't detect it means it can't be used for anything else.  So your computer is using the graphics chip integrated into the processor, and that chip is too old to run Sims 4, at least the current version.  You do have the newest driver for that chip installed, but the driver is from 2012.

You can certainly try connecting the monitor directly into the graphics card, which is the correct configuration anyway.  If Windows then detects the card, it should download an appropriate driver for you, and you can then restart and try to play.

The only other thing I can suggest here is you try to troubleshoot the issue with the graphics card.  That can mean taking it out, cleaning the motherboard slot and the card's socket for supplementary power if it has one, reseating the card, then blowing out the power connector and reconnecting it at both ends if the card does take supplementary power.  (If you don't know what I'm talking about, just look at the card: either it has a fairly prominent power cord inserted or it doesn't.)  If your motherboard has two PCIe slots, you can also try installing the card into the other slot, which would help if the first slot isn't working anymore.

If you can't fix your graphics card though, then you won't be able to play the current version of Sims 4 on this computer.  You can try downloading the Legacy Edition instead.  And you could in theory buy another graphics card.  But that would be a waste of money if the issue isn't your current card, and it might be a waste anyway considering the age of this computer.  At this point, any and all components could start to fail, and fixing or replacing them would cost more than the value of the computer itself.