This is really strange - I have this Dell Optiplex 7010 which one day stopped recognizing external disk drives. SD cards, USB Flash drives, external HDDs. I'm getting error code 39, and after researching it the only thing that came close was something about high filters and low filters. Well, that didn't apply to my scenario (no fix). So I resorted to the one thing that gave me hope was a 2 months old Acronis Image. The restore went fine, but surprisingly, the problem reoccurred right away (at the first login). At this point nothing makes sense.
USB works fine with other devices (printer, Wifi adapter).
USB works fine when booting to the Acronis recovery CD.
Dell diagnostics show no problems.
Updated all drivers, Dell drivers, the BIOS is current.
System UtilitiesWindows 7Storage SoftwareAcronisDell
Also: You might try downgrading the BIOS http://www.dell.com/support/article/us/en/04/SLN125793 and http://www.dell.com/support/home/us/en/04/Drivers/DriversDetails?driverId=V89FN. See if that helps.