Can I build something quiet for 180 quid?

Hi team.

I have decided to sell my ATV2 as it keeps bumming out with my TV. Its because the tv is quite old and does not have hdmi, so I am running HDMI to DVI and handshaking is a real pain, tried multiple leads but inevitably after what ever period of time it will no long sync and I get multi flashing colours on screen all the time.

So they seem to be going for a good price, which is nice. But I need something to replace. It will live in a bedroom so needs to be silent basically. I see stuff about raspberry and plenty of other stuff that says they simply are not up to the task.

So anyway I have lots of spare harddrives both 2.5 and 3.5 in so no need to purchase there. All stuff is on a server and i don't need wireless as there is ethernet next to it.

I need DVI output, analogue audio output and IR remote control.

Would prefer something off the shelf, second hand suits me but just such an array of stuff out there so not sure where to start, don't care if its windows. linux what ever, but it has to be able to run XBMC.

Any tips for the budget?