I'm no biology teacher, but I do teach culinary arts. What I tell my students is that they should almost always be able to use their senses to know when foods are bad. Smell it. It should smell very much the same as chicken broth/stock. If you're still not sure, taste a small amount of it. It will taste sour if it's bad.
I agree with the comment about boiling it. That can kill some bacteria that may be present. A great way to store stock is to reduce it, or boil/simmer it until it reduces in volume to just a fraction of what you started with. This gives you what we call "glace" (pronounced "gloss"), which is a great concentrate that can be frozen in ice cube trays and added to water, sauce, or soup as needed.
Good luck!