I felt exactly the same as you. I thought to myself. "This would be nice, if I could believe in it--but I don't. This doesn't work for me." Sorry about your animal! I'm actually the opposite - I don't really shed tears easily. I think the last time I shed a tear though, was in happiness, at my second born's birth, and before that, my first born's birth.
Glad to hear you're looking into the Dharmic religions. Hinduism is definitely work looking into, as is Buddhism. Sikhism is one that is often overlooked, but it's a nice path if one can get over being hung up on the Khalsa--the main problem for non-Sikhs when looking at Sikhism, it seems.