When the basement toilet tank fills up after being flushed, it stops and the water pipe vitrabes or makes noise. How would I get this to stop?
This sound's a lot like a bad fill valve. As the toilet flushes, the valve kicks in to refill. Once the toilet is full, the valve should slam shut -- if it is worn however, it can "chatter" or vibrate just as you've described. I'd recommend just replacing both the fill valve and the flush valve. These are easy projects that won't cost much and will get the toilet working properly again in no time at all. Good videos are here: http://www.fluidmaster.com/do-it-yourself/videos.