One of the toilets in my house will not flush. My stepdad can eventually clear it by pouring buckets of water and plunging and repeating until its clear. He is VERY cheap and won't pay someone to fix it and claims a plumber can't fix it because it's a problem the water company needs to fix. Would buying a snake possibly fix the problem or do I just need to call a plumber. Any advice would be great. Thanks.

A snake may work but it sounds like a closet auger is what you need or maybe a power suger that you could run througj your system. I do not know of any city that will clear a house drain. Their responsibility starts where your sewer drain enters the main.