Barry Tigner @ edn.com has a design idea on how to power a LED from a 1.5V battery using two easily available transistors.
A previous Design Idea describes a circuit that uses an astable multivibrator to drive an LED (Reference 1). The circuit in Figure 1 uses a simpler alternative approach. The circuit uses a 2N3904 NPN transistor and a 2N3906 PNP transistor, which operate as a high-gain amplifier.
Simple two-transistor circuit lights LEDs – [Link]