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Good to hear the brightness issue got resolved ... 
Yeah I didn't think about the relay details just yet haha ... I just realized that might be tricky too. Sounded much better in my head haha. It's a "chicken and the egg" problem and wouldn't work. Doh! This time I was stupid.
Ideally you'd want the power supply of the Arduino to shut down completely - why drain power when you're not using it.
Oh wait, maybe we could get that to work.
The Arduino is powered by your computer. Just have to make sure the USB doesn't remain powered when you switch your HTPC off.
If that is the case, USB power drops when you switch off your HTPC, then it might just work.
When the Arduino powers ON, we should tell it to "switch" the relay ON. On the pins that will be switched because of that we connect the power (110V or 220V) of the power supply that we use for the LED strips. So the LEDs will be power and switch ON.
When the Arduino loses power, the relay switches OFF, and therefore switches the power brick for the LEDs OFF as well.
To get this working we'd need to do some more research on how to switch relays with an Arduino. Optionally switching with a heavy duty transistor (MOSFet I believe), since the Arduino pins might not be able to drive the coil of a relay directly.
I did find this PDF, which would require yet another power supply, so that would defeat the purpose.
A good alternative seems to be a SSR (Solid State Relay), see this article. For 120V this item might be useful.
I found this article to be VERY interesting for that purpose as well.
If you decide to try these solution: please be careful to not fry yourself or blow up your Arduino/PC 
...
