The ''top cog'' is better refered to as the outer chainring (or big ring).

If the chain wont shift from the inner ring onto the big ring that suggests the outer limit screw (furthest screw from the frame) is in too WAY far, and needs to be turned outwards.

On the FD look closely at the bottom of the outer limit screw, atm it will be touching a stop on the FD. Back the screw off and the FD now has more room of travel. If its touching the stop it cannot travel any further. So the chain will not move up onto the big ring.

The outer limit screw comes into play once the chain is on the big ring. Its function is to prevent the outer cage moving too far and throwing the chain off over the big ring. So its purpose is to limit the travel of the cage.

When the chain is on the big ring, look at the small gap between the chain and outer cage. It should 1mm or less without rub if you spin the crank. If the gap is bigger, the outer limit screw needs to be turned inwards in small increments, so it will move the cage inwards to the desired position.