Depends on what you mean by media server...or file server for that matter.
What types of files? (Office apps, photos, videos)
What is the typical capacity? (Starting, goal)
What kind of media? (MP3, wav, video, streaming)
Will the machine be used for viewing the media? Or just server?
What network Speed? (100Base-T, 1000Base-T)
What Operating System?
A true fileserver can get by on relatively little CPU power.
Is size a factor?
Would a $50 motherboard, in a $25 case, with a $50 harddrive and $50 power supply meet your needs?
Sounds like it would, with the exception of the hard drive.
Maybe a cheap Althon on one of those older NForce boards (built-in Video) using a couple 120GB drives on a RAID card.
You can also watch for deals (and coupons) at major retailers / sellers.
No real specifics, I know. Just trying to figure out where your cost / performance cutoff is.