@RichZ, really? Everything I've read about composting, says not to add manure, meat, or bones because of parasites, bacteria, and other diseases. Plus those things attract rats. I don't have livestock, so maybe it's more common to add manure than I realize. Do you know about how long it should take to compost a 30+ gallon barrel of green and brown matter? Some things just aren't breaking down. Initially I had too much green matter, and it smelled horrid. So, I chopped up some cardboard boxes and cotton shirts for brown matter to balance it out. Those materials just seem super slow to break down all the way. I'm having the same problem with coffee filters.
The manue adds nitorgen, which speeds up the composting and heats it up. I've never heard not to add manure, except dog manure. If you don't have livestock, you can add some organic high nitrogen fertilizer. Mix it in well. adding lime also helps. Compost should just smell earthy, it shouldn't have a bad smell. the lime will help with odors.
You can buy a bag of compost starter at the Co-op and similar stores if adding manure makes you squeamish. It usually has alfalfa meal and some other nitrogen rich components in it. Some things take longer than others to break down in a compost pile. Cardboard and cotton fabrics are two of them. Fall leaves are one of the fastest brown materials to break down. Craft paper is another good one. Newspapers aren't bad either if you cut them up. I probably wouldn't have added the shirt unless it was made with organic cotton. There's no telling what chemicals are added during the manufacturing process.
I appreciate the info guys! I ordered a package of compost starter, which will hopefully do the trick. I also ordered some lime. @MichaelS, I hope it works out for you! I'm glad to know that I'm not the only one who has a compost pile that's not living up to its name.