Look, a V-brake can drag and act up in about as many ways as a (mechanical) disc brake. The mechanics are a bit more exposed, that's all. If you want to do it on the cheap, keep the wheel, keep the brake - just get it fixed. And learn to use the durn thing too. It's pretty easy to stop a car by down shifting and using the hand brake too, but you don't see many people doing that, do you?
While I can see valid reasons to stick with a rim brake(if that's what you've got), or to choose a rim brake when starting from scratch, there just isn't much good cause to switch from disc to rim - apart from exercising your freedom of choice.

The brake listed in the spec sheet seems to be a fairly decent sort: MTBR on Hayes MX4

It'll make more sense, while keeping you a lot closer to your $100 goal simultaneously.