What to do when you desperately want/need a calling or assignment but no one will
let you do anything despite being aware of your need?
The Lord has given each of us the responsibility to be agents unto ourselves. Having a calling in the Ward or Branch is always a good thing, but there are times when there are more needing people than positions of service. (You notice that I didn’t say worthy or willing people). Positions for service in the kingdom are always more for the benefit of the person serving in the position than they are for the people being served. But acting in a called position is not the only service that we can perform. The Lord has told us that we are agents unto ourselves—
Verily I say, men should be anxiously engaged in a good cause, and do many things of their own free will, and bring to pass much righteousness; For the power is in them, wherein they are agents unto themselves. And inasmuch as men do good they shall in nowise lose their reward (Doctrine & Covenants 58:28).
So we always have the opportunity of serving the Lord in ways other than fulfilling a specific calling in the Ward or Branch. And this is where the concept of real Christian service is at. So while you are not involved in fulfilling a specific calling in your own Church unit, find ways to lighten the burdens or to increase the joy and happiness of those around you. If you could do this anonymously it would greatly enhance the value of your service. You would be fulfilling the edict of the Savior, who said—
Let your light so shine before men, that they may see your good works, and glorify your Father which is in heaven (Matt 5:16).