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.
Compatibility
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 computers have a Thunderbolt port instead of a Mini
DisplayPort. Computers with a Thunderbolt port will have the following
symbol next to a port although the port physically appears the same as a
Mini DisplayPort:
Thunderbolt ports:
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.
It's very unlikely this will work unfortunately. It's a limitation of many graphics cards. Connecting the secondary external output will either not work, disable the primary output or clone both outputs. I'd definitely suggest testing it with another monitor if someone else you know has one available.
Alternatively, you can purchase external usb video cards that would allow for this. I've achieved this using a Toshiba Dynadock before however I have no doubt there are cheaper options. Good luck!
Best Answer
On your laptop while it is connected to the TV, see if the TV is being detected as a secondary display. You can do this by going to the Intel HD Graphics control panel. Open it by right clicking on the Intel HD Graphics icon in your notification drawer (you may have to expand it) and choose Graphics Properties. In the control panel, choose Display, then Multiple Displays from the sidebar. See if your TV is detected here. If it is detected, you will see a page with options to clone displays or extend desktop. If your TV is detected, then the single display option will most probably be selected, with your laptop display being the one. You can choose the TV in single display mode or choose to clone displays. This should work if your TV is detected.
If it is not detected at all by your laptop there may be a few causes. I will try to cover the ones that I can think of:
The cable may not be the right one for you. If you can, try it out with other device combinations (a friend's TV and/or laptop etc.) to see if it works. Try a different cable if you have/can borrow one.
Try the other HDMI ports on your TV.
Based on some suggestions in iFixit forum, you could try this. Apparently the power off delay works. Disconnect all HDMI sources from the inputs. > Unplug the power from TV/LCD for 10 minutes. > Plug the TV/LCD back in. > Connect the cable to your laptop. > Repeat previous step for each HDMI port.
Resetting the TV may fix it if it is a setting problem. (From the same forum). There is also apparently another way to reset it by holding the Exit button for around 30 seconds. I cannot test it out as I don't have a samsung TV: