It turns out it was, in fact, the battery! And my foolishness. Apparently I got the new and old batteries confused when I swapped them out upon receiving the guitar... I could tell because a new 9V from the same package that I have at home had a different expiration date than the one in my guitar; so I must have taken the old battery out, put it back in, then thrown the fresh battery in the trash. At least it was a cheap and easy solution.
Thanks everyone for the suggestions!