This feels like motherboard to me. How old is the computer? What's the specific model of the Dell System and/or the motherboard. Research "bad caps". A very common cause of premature motherboard failure is that manufacturers use low-quality capacitors which fail faster than higher-quality capacitors.
I would also spend a lot of time trying to make the system work with onboard video, as the chances that external video card functionality AND on board video going bad, both at the same time, is very low, IMO. Possible, but less likely. I'm willing to believe that all your PCI Express slots have all gone bad, but not that AND your onboard video also, all at the same time.
Give your motherboard a close inspection. Use a magnifying glass if you have one, and a flashlight. Pay particular attention to the capacitors and see if you can detecting any burst caps, swelling, leaking. Any kind of crud on the seams (it looks like light corrosion) means you have serious, catastrophic problems and you are probably wasting your time trying to fix it.
Having said that, I've replaced caps on electronics before. They cost about $1.50 each and it takes about 5 minutes to desolder and resolder a cap. I can help with identifying and sourcing parts if you want to go that route, but it's time consuming the first time out. If all you want is "pro level" repair, and the m/b is broken, throw the thing away and buy another.
If you can access the BIOS, find the part where it reports the voltages and temps and post them here. It's possible that your problem is a bad power supply and that the motherboard is still good. If you have (for example) 7 VDC on a 12 VDC rail, you could have problems like this. A new PSU might run $40 to $100, depending on quality and power output.