Hi, Craig,
Let me guess: your Dell is something in the Optiplex sereies, maybe a 780? I just connected up an 8-pin EPS power cable from my brand-new ToughPower GF1 750W to my Precision 3620's 8-pin power and 4-pin CPU (a bit of a stretch on the cables...) and PCIe Power to the installed GPU. It did nothing. My suspicion is that,without the 24-pin ATX cable plugged into the PSU there is something holding it out (not enough load, or a sense line for the power switch on the case which is only tied to that 24-pin cable. I have seen elsewhere that a 24-pin to 8-pin EPS12V adapter is needed to make this work, and I have such an adapter coming.
I do have a new GPU in the card cage, an Nvidia RTX 3060, and I did also plug in a GPU cable with the proper 8-pin connector for it. It's late. Tomorrow, I start by disconnecting the GPU power and removing it from the card cage. If it powers up at that point, Bob's my uncle. I might also bench test the supply with my PSU tester and see what's up with it.
It sounds like you and I are chewing some of the same ground, so maybe, between both of us, we can find the answer here.