Proteus Circuit LED does not work
ORIGINAL - NOT recommended. 

The original circuit is a lashup design with a number of shortcomings which make it hard to guarantee operation. The suggested alternative below is intentionally 'designed' at the same sort of level but has fewer compromises. (Diode OR gates, "interesting" reset cct). 

The original is designed to be  operated on about 9 Volts. It will not work on 5V (or less).

D4 is reversed as shown. Current must flow from +ve to gnd in direction of LED arrows. –    

Ensure there is power on the 4018 and 4011 circuits.

A 4011 IC typically has quite low current drive eg ONSEMI MC14001B 2.25 mA typical at Vdd = 10V (with 0.5V change in level when loaded). At Vdd = 9V, Vhi will be about 8.5V at 2 mA. Two red LEDs + 1K as shown should give slightly more than 2 mA. Red LEDs will operate but not very bright. 



ALTERNATIVE

The circuit below is 'out of my head' and untested but should work OK.  

Even if you do not build this circuit, just understanding it should teach you a lot - and the basic ideas can be used elsewhere. 

This is about as low level as the other circuit but uses (almost) no "tricks" and can drive LEDs to whatever brightness is required. It will run on 5V if desired.
This is offered mainly as an "idea starter"  but could be tidied up and refined slightly if thought to be useful. It should work as is.

IC1 is a CD4017 10 output decoded counter. Datasheet
It is clocked by an external clock as per the original or some other clock source.
When it reaches output 7 it resets to the start.
NB Outputs are shown as  1 2 3 4 5 6 7 ... but on IC are 0 1 2 3 4 5 6
Enable lines on CD4017 that are not driven need to be connected high or low as appropriate. 

IC2 is any driver IC that accepts high signals to enable an LED on the driven channel(s).
This could be 4 transistors or a ULN280x or similar.
ULN2803 data sheet
As the ULN280x drivers have 8 drivers a single IC can be used for 2 dice (4 drivers each). 
7 LEDs are driven in a die / dice shape.
LEDs are numbered 1...7 and arranged as shown at bottom right.
The array at top right has the LEDs in the array arranged in order 4 1 7 3 5 2 6 as shown.
There are only 4 groups of LEDs.
A is centre spot, used for numbers 1, 3, 5
B is left top, bottom right used for numbers 2, 3, 5, 6
C is the other diagonal
D is the 2 centre horizontal LEDs.

The only trick is the use of 13 diodes as OR gates.
Fewer diodes could have been used by using LEDs in series but littl would be gained and it's harder to follow.  

CD4017 output 1 drives channel A = centre spot = dice-1  

CD4017 output 2 drives channel B = which drives LEDs 1 &amp; 7 = top left and bottom right = dice 2.

Here is where the fun begins :-)

CD4017 output 3 drives channels A AND B via two diodes so LED 2 is lit by channel A and LEDs 1&amp;7 are lit by channel B so in total 1 2 7 are lit = dice-3

And so on.

CD4017 output 7 going high places a high on the Cd4017 reset pin via reset diode and output 1 is selected. The reset time is arranged to be short compared to clock rate.
A 0.01 uF cap and 10k pull down are shown but adjust to suit clock speed. The cap is used as without it the IC may start to reset and then remove its drive and so achieve a partial reset. While there is no formal hysteresis here it does in fact work very reliably in practice. 

The CD4017 could be one with a Schmitt triggered clock but this is probably not needed in practice in this application. 

This circuit does not have the LED drive limitations of the original. 

Total parts for 2 dice is
1 x ULN2803 driver, 2 x CD4017, 14 LEDs, 14 x iN4148 diodes, 8 x R, 1 x c, clock source.