Dell XPS 8300 GPU issues

I have had a Dell XPS 8300 since 2011.

The specs are:

Intel i7-2600 Quad Core 3.4ghz Processor

460w PSU

8GB RAM

Sapphire AMD Radeon HD 5670 1GB GDDR5

My issue is that my video card is dead after 4 years and I need a replacement just as good, or better, for under $100. At first, I thought it was easy. Ordered a GT 730, a nice entry level card a bit better than the 5670 and more power efficent, and went through the process of installing it. Uninstalled AMD drivers, switch video cards and it fit perfectly. The problem is I just get a black screen on boot or, sometimes, the Dell splash screen.

After hours researching I discovered it won't work because the motherboard, 0y2mrg, and it's bios, A06, are incompatible with newer GPUs. Seriously? Rarely have I ever heard of this problem. The last update was back in 2011, the same year I got this PC when it was new. What the hell is with the lack of support?

Whatever, I'll just find something that is compatible, but this is proving to be unnecessarily difficult. People who asked the same question were either answered from a couple years ago and outdated or unanswered. I've seen the Dell approved cards and they are ridiculously overpriced for what they are. The 5670 is a super low end card and was even released as one back then, but Dell wants to sell it for over $200?! If I try to look it up on other websites, like Amazon or Newegg, it's almost impossible to find or also too costly.

My question is this, what is a good video card that costs at most $100-$110 that works with the Dell XPS 8300 motherboard and does not require any other parts to be changed?