You can base the desparation on a non - sexual situation such as a character's desparation to save their family business from bankruptcy. Detail their attempts to find solutions, the sleepless nights, the meetings with creditors. Their desparation can be shown through their dialogue, for instance, pleading with the bank for an extension. You can also use descriptive language to paint a picture of their forlorn state, like 'His eyes were sunken, a sign of the many nights he'd spent worrying about the future of his family's legacy.'
To write a desparation - themed story without erotic elements, consider a setting like a post - apocalyptic world. The character is desperate for basic necessities like food, water and shelter. Describe how they scavenge, the fear they feel when facing other desperate survivors. You can show their desparation through physical actions such as their trembling hands as they search through the ruins. Also, use their internal monologues to convey their desparation, like 'I don't know how much longer I can last in this desolate world.'