There is probably a few different ways to wire this up.
First, if your cabs power button is switched, not momentary, you could splice into the green wire that goes from the PSU to the motherboard as the green wire is usually PWR_ON. Be careful though as Dell is famous for having proprietary pin outs on their PSU's, so it could be grey or purple. Having said that, just connecting the wire with everything else turned on, might not force it to send power.
If that doesn't work, hop in the BIOS and look under the system or power options and look for a setting that says something like "Turn on when power is sensed or restored" or "Return to original state after power loss". This way, you could add a switch from your incoming power (from your house, before PSU) and just turn everything off and once you turn it back on, computer will turn it self on. Only problem with this is the OS is not following proper shutdown sequence and could cause damage.
If your cabs power switch is momentary (which from the description of your post, it probably is), pop the front off of your Dell and splice into the front mounted power button. From the pictures online, it looks like it has a front mounted power button, so there is no reason you can't splice into it. *Some google flu reveals that the power button might not have a wired connection to mobo at all, it is a plastic arm the presses a button on the board itself*. I think there is a daughter board hiding behind the front cover that houses power button/LEDs/USB/mic and earphones making it harder to pinpoint the correct wires to short out.
Just throwing out some ideas, let us know what you come up with...good luck.