Ok, well... no answers. I've found a place locally that was selling a power supply so I got there with my server, I told them I would purchase the PSU only after I confirm the fault was actually the power supply. Well, what do you know, the unit started properly with the new PSU, now in IDRAC I see both power supplies but on the faulty one it reads "present, input lost"  So the answer is YES, a power supply may be faulty even if the green light is on. 
Hello, I tried to find answers on the forum but nothing so far I have this R710 at home that I use as a media server, it was running fine before a power failure the other night (no I don't have a UPS :-( When power got back, I noticed one of the PSUs light was off, so I took it out of the unit, but still the unit won't turn on. I still have one supposedly good PSU because the little green LED on the mobo turns on, and I can access the iDRAC, this feature I didn't know before searchin the net for answers, I'm kind of novice with servers. When I access the iDRAC, on the power supply page, I see nothing, no power supply listed. Is it possible that a power supply maybe "half bad", enough to work the standby circuits but not the mains?  Symptoms: Unit won't turn on. Can access Idrac functions, but does nothing if I try to turn it on via the "quick launch tasks" Power supplies are not visible on the Idrac pages. Front display works. Server was fine just before a power failure that took one of the PSUs The remaining 870 PSU has the green light on, and the fan runs for about 2 seconds everytime I remove power from it.  Thanks for any help.
Dell R710 does not start after power failure