That is an extremely tight budget. I really don't think I'd bother with that little. If you already have at least a case to put it in or a hard drive to re-use then it might be possible, and I don't think you're going to be able to afford Windows, so it'll be Linux for sure. My go-to site for PC builds is Ars Technica. Here's a link to their latest Budget Box Guide, which they target $700, including monitor:
http://arstechnica.com/hardware/guides/2009/10/the-budget-box-october-2009-edition.arsI recommend checking their CPU and Motherboard Technologia forum. That's where most PC Build questions end up.
Let me see what I can put together at Newegg:
Case: This is actually the hardest part on a cheap build because you pretty much have to get one with a built-in power supply, which typically suck. Find something with around a 250-300watt power supply that you can tolerate. Maybe the Foxconn TLM776 at $40.
Motherboard: I would look for an AMD motherboard with a 780G Northbridge, as recommended by Ars. The cheapest one I see at Newegg that I'd be comfortable with is the ASRock A780GXE at $65
Processor: For DF I'd probably go with the Athlon II X2 250 Regor 3.0GHz at $67. A Phenom II would be good, but the cheapest is the X2 545 at $93.
RAM: Wow, it looks like RAM has gotten expensive lately. I'd normally recommend 4 GB of DDR3, but the cheapest you can get that is $84. You may have to start out with a 2 GB stick and add another 2 GB later. The cheapest there is $39 (and Crucial is actually a pretty decent brand). RAM prices change frequently, this may drop heavily in month or so. I'm surprised it's that expensive.
Hard Drive: I wouldn't normally recommend getting less that 500GB now, but DF obviously doesn't need that much. Still, it seems silly to go less than 250GB. The cheapest 250GB is a Western Digital Caviar Blue for $45. That works for me since I happen to like Western Digitial, although I usually get their higher end drives.
This will make a complete computer as the audio and graphics are on the motherboard. My only real reservation about it is the case (especially the power supply) and the RAM. Adding more RAM is pretty easy, but moving everything to a new case is not. At some point you'll probably want a graphics card, but the onboard graphics should be adequate for now, and certainly fine for DF.
The total there before tax and shipping is $256, so I came close. You could actually drop the processor to the 240 and be under $250 base price. The shipping will probably hurt though, especially with a Case involved.
At this price point you can often get better deals from the big manufacturers. Dells 2 cheapest Inspiron Desktops are both $249. The base model Inspiron 546 is reasonably close to what I specced out, but the processor is significantly weaker (and upgrading to the X2-250 costs $90 -- more than the processor itself actually costs). Still, you would get Windows with that, so it's not horrid.