The Weber IMB carburettors fitted to the 500s are a relatively simple devices when compared to some of the other contemporary carburettors fitted to other Italian cars (eg: DCOEs).
I've had a dig around and come up with some information that I hope will help.
The first picture is a general 2D schematic of the IMB series of carbies. They are all constructed similarly with the only difference between say an 26IMB1 and a 26IMB4 being the tunable components (jets etc.)
The idle circuit works thus: When idling, fuel is carried from well 23 through the passages shown in the second picture to the idle jet (13) where it is mixed with air coming in from inlet 5. Through duct 3 and idle speed orifice 18 - which is adjustable by taper-point screw 17 - the fuel reaches the carby throat just past the throttle butterfly 19 where it is drawn into the general mixture. From duct 3 the mixture can also reach the carby throat through transition hole 20 thus permitting a smooth transition from idle to full power as the butterfly opens. The diagram and description are courtesy of the Fiat 500 Shop Manual.
The second picture is of a spare IMB and shows the positions of the idle jet holder (A), the external fuel galleries in the idle circuit and their lead plugs (B) and the idle needle taper-point screw (C).
The last picture shows the idle jet holder and the jet itself.
If your car will not idle, but otherwise runs OK both hot and cold, then the problem is likely to be along this circuit somewhere.
It is possible that the galleries are blocked with general crap and need cleaning (again). You may have to drill out the lead plugs to clean the galleries properly. The plugs can be easily replaced using appropriately sized lead buckshot.
Maybe the jet is blocked - if so, soak it and blow it out with air, do not ream it or you'll ruin it.
The air feed may also be occluded, though this would be unusual.
I think your only alternative is to remove the carby, strip it and clean it again.
Let us know how you get on,
Chris