1990 Toyota Corolla Engine hesitation

The engine cranks smoothly but no idle. If idling speed is increased at 2000rpm the machine runs but lacks power and runs with hesitation. I tried to clean all fuel lines, bring down the gas tank and clean all hoses and tubes running from it to the fuel filter, checked fuel pump for fuel discharge when engine is cranked, seems okey. Bought a carburator repair kit and overhauled the carburator. Replaced High voltage distributor assembly and sparkplugs. Noticed a burnt solenoid like part attached to the large hose in the vaccum line and on a cylinder like part where the fuel line hoses the supply and return pass through.
What is the function of this burnt out part? Could this be the cause of my engine problem? How do I check if this part is causing the problem?