It could also be done with 555 astable timer, 4040 binary counter and 4013 flip-flop. Put a switch to the input of the flip-flop, and the output to the trigger pin of 555. When you push the switch, the flip-flop output goes high and the 555 starts oscillating. Set the 555 to output about 2Hz signal into the clock input of 4040. The first output stage of 4040 is now giving a signal of 1Hz, which can be used to drive a transistor which then drives the LED. Every further output will be at half speed of the previous one, so the 12th output stage of 4040 will go high after 2048 pulses (about 34 minutes with 1Hz signal), and that pin must be routed to the reset pin of the 4040, and to the flip-flop to turn off the 555.
However, this will likely not fit into such a small space you described. :\