Not really a cab, but here's a portable retro game solution I made a long time ago. It's since been updated with Xbox 360 controllers but the whole thing set me back about $25.
As for a cab for $20 or less....well you're pretty much out of luck unless you can find a cab that someone is giving away. A buddy of mine found a couple of empty Golden Tee cabs in a dumpster once that he rescued, so his was free