I did the same thing except i used a 4.2v Lithium Battery (2.6amp/h).
Got nothing, while using Softserial, as soon as i moved to a regulated 5v in (not a slowly dropping voltage curve from an unregulated battery supply)
My solution this problem.
Use a 5v regulator from a a couple of batteries in series to produce around 7v, then drop the voltage down, you'll find your chip springs to life, these chips really don't like anything but a regulated source.