if the logic part is checked correct,
the failure could be attributed to lack of filtering of Vcc line .
I would suggest
1. to have one 0.1uF capacitor across each IC that you have used.
2. the 5V regulated supply can be decoupled properly by say 470uF/16V capacitor after regulation.
3. reduce current demand of Seven segment displays by increase of series resistor by selecting efficient displays
with these precautions , the practical arrangement would also work, with a battery used
Now comes the issue of noise induction from the Vcc derived using power brick. in such cases, you might have to prevent noise from maims line by an input filter. The diode bridge can have 0.1uF capacitors wired across each of the diodes. The resultant DC(both output and return wires) can be connected to the board, after winding few turns through a toroid core. this would help any possible rf interference on these wires due to strong local Radio/TV stations.
All the best