Based on the information provided I would say is a a problem on the front panel header, cables for the front panel header or/and power supply., but first try to isolate the problem, checking first the software part . I would recommend checking with the guy from DELL* they are the system manufacturer and should be able to provide you with detail for troubleshooting or at least determine what is the prob. Give it a try updating the BIOS on the board it always a good idea with this kind random no-boot problems.
I'm probably way late answering this, but I had exactly the same problem with exactly the same model of computer. Swapped the power supply for a known good one and the problem went away.
Solved the problem, rather a long time ago in fact. Just changed the PSU - then starts up every time.