@nibble123, joeschmuck has what's probably the most economical build that would meet the hardware recommendations for FreeNAS. To match it, you're looking at about $60 for the motherboard, $110 for the CPU, and $160 for RAM--you're at $330 already. Case and power supply are completely at your discretion, but would obviously add to your total. If you actually have 10 TB of data you need to store, and you want redundancy, the bare minimum you could get away with would be 4 x 4 TB hard drives ($180 ea., $720 total) in a RAIDZ1 configuration.
Another option that seems somewhat popular is a used HP Microserver N40L. You can get those on eBay with no drives for about $300, but you may still need to upgrade the RAM to a bare minimum of 8 GB (and 16 GB would be better given the capacity you're talking about).
Even if your stated budget excludes the drives, you're pushing the margins of what's feasible with FreeNAS. You might try looking into other software solutions like unRAID or NAS4Free, as they may be less demanding of your hardware.
Edit: If you're willing to consider used hardware, you have more options, though you're going to pay in terms of decreased performance and likely higher power usage. You may also find that parts are more expensive than for a current-production machine--older-spec RAM, for example, tends to get expensive. But with that said, it may be an option to consider.