Time delay on circuit
The circuit as given will stabilise with Q1's base around 600mV, which scarcely turns it on.  That explains why you get no significant power to the load.

Reducing R1, R2 and R3 to a tenth of the given values solves that problem sufficiently to light the LED, though it would also shorten the time constant.  This can be compensated for by increasing C1 by the same factor, to 1000µF.

If a further increase in load power is needed, connecting a second transistor in Darlington configuration might work.  You'll need to adjust the timing components for the higher base threshold.

In general, timing long delays using purely discrete, analogue components is fraught with difficulty, especially if you then want a sharp turn-on of a relatively heavy load.  Consider using an IC specifically designed for the purpose, such as the 555.