USB can provide 5V and 0.5A on a single connection, for a total of 2.5W. Consumer 3.5" hard drives draw around 7 or 8 watts while idle, with a little variation around that number depending on the specific drive. That suggests that a single USB port simply cannot power a SATA hard drive on its own, and all available 3.5" hard drive enclosures bear that out.
Some 2.5" drives, however, can be powered out of a single USB port.
It does matter what size the drive is. Large 3.5" hard drives require more power then what even two USB ports can provide. For reference, a single USB port can provide a maximum 500 mA of current. A Western Digital WD3200AAJS, on the other hand, requires 1444 mA at idle, and 1608 mA when reading/writing files to/from the drive.
It is part of the USB specification that if a device attempts to draw too much power, it is simply disconnected from the target system - this is why, while your adapter itself shows up, you can't access the drive. There is no jumper setting to change, SATA drives don't have any.
What you're trying to do is, quite bluntly, impossible. You'd need the power of almost four USB ports to get the HDD working, which is also why you never see full 3.5" drive enclosures without an external power supply.
Your only option is to power the drive from the computer, power it using an external power supply, or if you can find any (reliable) +5V and +12V DC source, you could hack together your own. Or you could just buy a USB HDD enclosure that has the power source.
Best Answer
You can't simply plug a USB cable into 12V instead of 5V - chances are, you'll just fry something: Best case only the USB/SATA adapter, worst case the mainboard of the Computer.
SATA Adapters with only USB power supply are by design only usable for devices, that can be powered by USB - these are all SSDs I know of and the majority of 2.5" drives. The 3.5" drives not only need another voltage (which could be created via a step-up converter in the adapter), but due to the much bigger mass of the platters also a much larger amount of power to spin them up. USB is not able to provide that amount of power.
So, long story cut short: You can not use this adapter with 3.5" drives.