Jaycar short circuits Vol.1 bonus project 2: 3.5 minute timer
This seems to work pretty well, it's got a fairly crispy edge, and I put the switch in series with the positive rail so the battery won't be wasted when the LED is off.   

The LTspice circuit list follows the drawing just in case you want to play with the circuit.



Version 4
SHEET 1 880 680
WIRE -736 -2176 -880 -2176
WIRE -448 -2176 -736 -2176
WIRE -272 -2176 -448 -2176
WIRE -80 -2176 -272 -2176
WIRE -736 -2144 -736 -2176
WIRE -448 -2128 -448 -2176
WIRE -272 -2128 -272 -2176
WIRE -80 -2128 -80 -2176
WIRE -80 -2032 -80 -2048
WIRE -80 -1936 -80 -1968
WIRE -272 -1888 -272 -2048
WIRE -144 -1888 -272 -1888
WIRE -272 -1856 -272 -1888
WIRE -448 -1808 -448 -2048
WIRE -336 -1808 -448 -1808
WIRE -448 -1776 -448 -1808
WIRE -736 -1728 -736 -2064
WIRE -688 -1728 -736 -1728
WIRE -560 -1728 -608 -1728
WIRE -512 -1728 -560 -1728
WIRE -880 -1680 -880 -2176
WIRE -736 -1680 -736 -1728
WIRE -560 -1680 -560 -1728
WIRE -880 -1552 -880 -1600
WIRE -736 -1552 -736 -1616
WIRE -736 -1552 -880 -1552
WIRE -560 -1552 -560 -1600
WIRE -560 -1552 -736 -1552
WIRE -448 -1552 -448 -1680
WIRE -448 -1552 -560 -1552
WIRE -272 -1552 -272 -1760
WIRE -272 -1552 -448 -1552
WIRE -80 -1552 -80 -1840
WIRE -80 -1552 -272 -1552
WIRE -880 -1488 -880 -1552
FLAG -880 -1488 0
SYMBOL LED -96 -2032 R0
WINDOW 0 -45 32 Left 2
WINDOW 3 -96 64 Left 2
SYMATTR InstName D1
SYMATTR Value NSCW100
SYMBOL Misc\\battery -880 -1696 R0
WINDOW 123 0 0 Left 2
WINDOW 39 0 0 Left 2
SYMATTR InstName V1
SYMATTR Value 9V
SYMBOL res -96 -2144 R0
WINDOW 0 34 48 Left 2
SYMATTR InstName R6
SYMATTR Value 270
SYMBOL cap -752 -1680 R0
SYMATTR InstName C1
SYMATTR Value 200µ
SYMBOL res -752 -2160 R0
WINDOW 0 47 55 Left 2
WINDOW 3 38 80 Left 2
SYMATTR InstName R1
SYMATTR Value 1meg
SYMBOL npn -144 -1936 R0
SYMATTR InstName Q3
SYMATTR Value 2N3904
SYMBOL res -256 -2032 R180
WINDOW 0 -43 61 Left 2
WINDOW 3 -48 34 Left 2
SYMATTR InstName R5
SYMATTR Value 10k
SYMBOL npn -336 -1856 R0
SYMATTR InstName Q2
SYMATTR Value 2N3904
SYMBOL res -432 -2032 R180
WINDOW 0 -38 65 Left 2
WINDOW 3 -45 37 Left 2
SYMATTR InstName R4
SYMATTR Value 10k
SYMBOL npn -512 -1776 R0
SYMATTR InstName Q1
SYMATTR Value 2N3904
SYMBOL res -576 -1696 R0
SYMATTR InstName R3
SYMATTR Value 820k
SYMBOL res -592 -1744 R90
WINDOW 0 0 56 VBottom 2
WINDOW 3 32 56 VTop 2
SYMATTR InstName R2
SYMATTR Value 1meg
TEXT -852 -1520 Left 2 !.tran 250 startup uic