I wonder if this has something to do with the latest firmware… I have the same issue. When I plug-in the power supply, the fan turns on immediately (very loud) but the drives and front lights do not power-on. There is a dim flashing green light on the power switch. The light on the power supply / cord is solid green. Flicking the power switch on/off makes no difference (fan stays on). This happened a day after updating to the latest firmware (2 days ago) and replacing one failed drive (the recovery process completed and all lights were solid green - I left it for a day turned on with no further activity then I saw this situation with the fan being loud and no other lights working).
I found this video on youtube from another Drobo customer, this is exactly how mine behaves: https://www.youtube.com/watch?v=Bsp0y6UIfCU