I'm not sure what "oxidation connectors" are, but you're probably asking either one of two things...
If you're asking about using a card with your Dell that doesn't have the PCIe power plugs on the card, then yes, you can. The motherboard is is designed to supply power to any PCIe compliant card via the PCIe slot, and any PCIe 16x card without additional power plugs on it that will fit into the slot will work. You can also use PCIe 1x and PCIe 8x cards as well.
If you are asking about using a card that does have the PCIe power plugs with your Dell that doesn't have the corresponding power cables on the power supply, then maybe...
You really don't want to run a card that has those plugs without power going to them. However, if your power supply has the ability to provide the card the power it needs you can use a standard 4-pin molex to PCIe adapter and be fine. I installed a 9800GT into my mom's Gateway PC that way, and it works fine.
I guess you could also be asking about a third option involving a PCI card, and not PCIe at all. In this case, yes, you can ran a PCI card in your Dell provided it has a PCI slot.
This is about the best info I can give you based on what you asked. AT forums may be able to better answer your questions if you tell us what specs your Dell has, and what you're trying to do with it.