Need to upgrade My Video Card


Tech Monkey
My computer is an Asus Republic of Gamers PC, about ten years old, and it's come to the point where it won't play the AAA titles that are coming out like Doom Eternal, Cyberpunk 2077, Farcry 6, and even Borderlands 3 is just beyond my specifications. Talking about specifications, here they are for my PC:

Intel Core i7-3770k CPU 3.50Ghz
NVIDIA Geforce GTX 670

I'm unsure as to whether I should just upgrade the video card, and what card to upgrade to, or get a new PC. I'm leaning toward getting a new video card. Unfortunately, the connection on the motherboard is PCIe 3.0, although I read that you can still use a PCIe 4.0 card in a 3.0 slot. It just won't operate at top speed. Is this correct?

I don't want to spend too much money. I just want a card/PC that will be able to play games like the ones I mentioned.