This begs for a 6 pin microprocessor like the Microchip 10F200. The outputs will drive up to 25 mA, easilly enough for a typical LED. And it will run on 2V to 5.5V.
But you want a small battery. A typical LED will kill a small battery in short order. You'll need a super efficient LED, running around 1 to 2 mA, to last for any length of time. Two AAAs will give you enough voltage to run the chip and enough power to run the high efficiency LED for several minutes.
However, you'll have to write the code for this, buy a programmer to put it in the 10F200, and then solder the chip to a board with the LED, a limiting resistor and a reset switch. By the way, this does come in an 8 pin DIP package, which is large enough to put this, and the other components, on proto boards you can buy from Radio Shack.
I can't begin to concieve of a way to do this in an analog circuit without making my head hurt.
End two cents.
kenjj