$150? Eh...not sure that's possible even with older hardware. I certainly wouldn't get anything below a Wolfdale/Yorkfield Core 2, unless its a novelty build. But of course, those Core 2 parts and their successors have done a good job retaining their value on the second and firsthand markets.
The main killer though will be the hard drive. Even a sub-1TB drive is likely to not be exceptionally cheap. And then there is the power supply which is another $40-50 or so if heavy gaming is not ever expected to be a goal.
If you buy all the basics (CPU, motherboard, 100-250GB HDD, power supply, case, CPU sink+fan, ultra-cheap video card, optical drive) carefully you MIGHT be able to get away with a $300-350 minimum build, unless you can get certain parts for free. Before software of course.