Talk about overkill.
You could get a 2nd hand Pentium II system for about a tenner. Add a SATA or ATA100 controller card, a couple of hard drives and you'd be set.
And a screen for a download box? Are you mad?

You could use an ssh terminal under linux, or VNC/remote desktop/pc anywhere/whatever under windows. Or just buy a KVM switch.
PII's can be passively cooled, get a couple of silent drives for the HD's, get a small psu that is quiet and you'll be set, put it in a decent acoustically lined case and you wont be able to hear it atall.
My download box used to be a PII 450, 250W PSU, 256MB RAM, 40G HD, 8MB Gfx Card and a 10/100 NIC all running under FreeBSD.
£600 is Mini ITX or Mac Mini material if you want something discrete. :/