Looking for a HTPC to install in a museum to display a 1080p video from a projector, how demanding is it?

I work in a 3d studio and we are currently working on a video that is going to be displayed in a museum. We have negotiated a package deal so that we purchase and install everything they need. I have been asked to find a suitable HTPC to use, but I'm not updated on the current capabilities of low end hardware these days.

I have been told that it needs to be able to say on 24/7, it will be hidden behind a projection screen, but it should have adequate ventilation. It will only play a 8 min video on loop with eiter 2.1 or 5.1 sound. Can your run of the mill low end HTPC deal with this, my highest concern is the 24/7 operation, it will be restarted and be shut down every now and then, but it will mostly stay on.

My boss told me he would like something for about 200$, is it possible at this price point?

Thank you for any help you can give me.