Dell 540 Studio PSU replacement

That connector would go to a graphics card (if you have one that takes additional PCIe power). If you do not have a graphics card, that connector can be left loose. Here is a link that shows the different power connectors used within a PC (and even some old ones no longer used) http://www.playtool.com/pages/psuconnectors/connectors....
Hope it helps

Thanks! I know when I disconnected all the PSU wires, this connector was connected to an area that was the power button. However, I don't see an way to get this connector back in the same area. It's the identical connector, but I just don't see anything for it to plug into.

For your power connections, you should have something like this going on.
1) 24 pin Main Power connector into the motherboard - only one place to fit that.
2) a 4 pin ATX (CPU) connector into the motherboard - upper left hand corner - you want to use a 4 pin, 4+4 pin (just one) or an 8 pin (which will hang over nothingness for half the connector) ATX connector
3) Power to optical drive(s)
4) Power to HDD(s)
5) Power to fan(s) that aren't connected to motherboard
6) Power to graphics card(s) if any (that's the PCIe connector)
Any other power cables can be bundled up and tucked away, you should be good to go at that point.