I'm afraid the only real answer is probably trial and error. There are some people who are tone deaf and others who just lack musical training, but can learn how to sing on pitch. I think the number of people who are truly tone deaf is pretty small. Yup, just found this article I remembered hearing on NPR several years ago (http://www.npr.org/programs/atc/feat...tonedeaf.html). Most tone deafness is due to physical trauma, illness, or deformity. If you don't have those, then the chances of you being truly tone deaf are pretty slim (The woman in the article was the first documented case, so there you go).
You might be able to go to an ear, nose, and throat specialist and find out, or they could point you in the right direction. Either that or a vocal instructor, but depending on the musician, some of them can be pretty snooty. If you can find a nice one to work with who isn't condescending, then that's the way to go. They should be able to tell you within a few sessions if there's hope for you or not.