This paper investigates a finite-source retrial queueing system characterized by request collisions, primary server unreliability, and the inclusion of a backup server. In cases of collisions, when a new job arrives while the service facility is occupied, both jobs are sent to a virtual waiting area called the orbit. Customers in the orbit make further attempts to access the server after a random interval. During server breakdowns, the customer at the server is transferred to the orbit. The system consists of a backup facility when the primary server is unreachable to process requests while the main service unit is under repair. The novelty of this study lies in the implementation of the impatience of the customers and conducting a sensitivity analysis using various service time distributions for the primary customers. We analyzed two scenarios, presenting key performance metrics through visual representations to emphasize the observed differences.