Well, AGP is kind of defunct these days. One thing to be absolutley sure of is what sort of AGP slot you've got. Is it a 4x or 8x type. Most modern AGP cards require an 8x slot and despite a lot of them having "4x/8x" written on the packaging and the specs alegedly being backwards compatible they have a massive shit fit when they actually meet a 4x slot.
Moving on, you say "Dell video slot"??? Now that's something I've never heard of personally but considering you have PCIe x1's I wouldn't be surprised if this is a PCIe x16. It might be a good idea to punch the model number in to google and see what (if any) reviews of it exist as they'll refer to components in standard terms; rather than marketting ones.
If none exist, be cheeky. Phone Dell sales and tell them you want to upgrade your machine (or if it's a current model play with the website) and if it starts offering you PCIe x16 cards as options... you're a winrar as I believe the meme goes.
And no, I've yet to see a full on GFx card use a x1 slot, I'm sure they exist in some fashion somewhere but never seen them; I have seen capture cards (Hauppage HVR's and such) make use of them though.