You should be able to find a stripped down older server and build it back up for sub $100.
Because the offers change so frequently and are at such a variety of places, it's best to run the search yourself.
Go to google shopping. Search for "1u Server" and filter for the price between $10 and $100. Most of what you'll find are boxes that are about 5 years old that have had the memory and/or drive stripped out of them. From there, you have to go to your favorite trusty hardware vendor like newegg and find compatible memory. You probably have a spare drive laying around somewhere.
For what you pay and what any reasonable person would expect performance-wise, I've been pleasantly surprised with what second hand servers can do. Performance-wise, they'll meet any need an Atom would meet. They tend to be power hogs though.