If the Wikipedia article is to be believed (and I do believe it is correct based on what thunderbolt is), then your configuration will not work.
Apple Thunderbolt Displays, like the video input on Thunderbolt iMacs,
drop compatibility with all previous standards, including VGA, DVI,
and DisplayPort.3 As such, they cannot be connected to computers
lacking a Thunderbolt port, including pre-2011 Macs and the vast
majority of PCs.
Thunderbolt is not the same as Display Port. Therefore you can only connect thunderbolt equipped Mac's (or some PC's with thunderbolt hardware and appropriate drivers) to the Thunderbolt display.
From the Apple Mini DisplayPort FAQ
- My computer has the same connector but the symbol is different, what does that mean?
Some Apple computer have a Thunderbolt port instead of a Mini
DisplayPort. Computers with a Thunderbolt port will have the following
symbol next a port although the port physically appears the same as a
Are compatible with all of the Mini DisplayPort adapters referenced
below in question 5 and with Apple Mini DisplayPort equipped displays.
Support adapters like Apple's Thunderbolt to Gigabit Ethernet Adapter
and Thunderbolt to FireWire Adapter which are not otherwise compatible
with Mini DisplayPorts. See Thunderbolt ports and displays: Frequently
asked questions (FAQ) for more information on Thunderbolt.
So with your adaptor you can drive a DisplayPort based monitor to your PC, but not a thunderbolt display as it lacks support for DisplayPort. That's why it didn't turn on and work.
Some Googling and I haven't yet been able to find a USB based thunderbolt adaptor, it seems there is talk of such a device using USB 3.0 to thunderbolt although at reduced speeds. There are a few thunderbolt PCIe cards available and some PC motherboards support thunderbolt.