I've seen symptoms like this cause by things ranging from a dead RAM stick to a malfunctioning power supply. Could also be an overheating protection mechanism. In fact I recently came across a similar issue just today.

Take out all the nonvital hardware. If there is more than one stick of RAM, remove one and leave the other in. If that doesn't work, swap it out for the other stick and try again. That checks RAM.
If not, then there's a good chance (but no guarantee) that it's the power supply, and that should be checked next. For a power supply or overheating fault, try pulling the power cable from the back of the computer for 10+ seconds, then plug it back in and see if that works. You can also buy a power supply tester quite inexpensively.

Then I would test the functionality of the power button at the front. I'm not 100% sure how the D5s behaves normally but the lights might just show power but not that it's actually "on" and I've seen power buttons fail (on my own home computer I had to swap my reset and power on buttons - the reset button is nonfunctional)
Beyond that, a dud motherboard is not as common but it happens and the symptoms fit as well as the other issues.