If anything I would think that would prove that the valve (itself) is NOT sticking.
On the T piece, on the top of it there is a brass pin. When it is pushed down the water stops, when it rises up the water flows. If there is nothing holding it down then it should move up. Sometimes these get stuck and gan be released by manually pushing the pin down and gently pulling it up a few times, but beware that the pin only moves amybe 3-5mm anyway.
However you have said that you heard water going into the rad as you unscrewed the top section, which would say to me that as you start to remove the top (that is currently holding the pin down), the pin is starting to rise, and that when you completely remove the top the pin will likely have risen to it's full height and water will flow into the rad.
If thats the case then just inspect the top plastic bit. When you adjust the temperature setting on it the inside of it should move up / down slightly, (this is what controls when the thermostat section pushes on the pin to stop the water).
I guess it's possible that the actual thermostat section of the TRV has gone faulty and isn't releasing the valve, in which case it's easy to replace as you can just buy a new TRV and swap the heads. - Strange thing to happen though I would think.
Of course the other option is that your house was already so hot that the TRV was operating correctly and keeping the rad switched off, but if you had set it to it's max then I believe it is supposed to keep the rad on whatever the temperature.