Today's digital data storage systems typically offer advanced data recovery solutions to address the problem of catastrophic data loss, such as software-based disk sector analysis or physical-level data retrieval methods for conventional hard disk drives. However, DNA-based data storage currently relies solely on the inherent error correction properties of the methods used to encode digital data into strands of DNA. Any error that cannot be corrected utilizing the redundancy added by DNA encoding methods results in permanent data loss. To provide data recovery for DNA storage systems, we present a method to automatically reconstruct corrupted or missing data stored in DNA using fountain codes. Our method exploits the relationships between packets encoded with fountain codes to identify and rectify corrupted or lost data. Furthermore, we present file type-specific and content-based data recovery methods for three file types, illustrating how a fusion of fountain encoding-specific redundancy and knowledge about the data can effectively recover information in a corrupted DNA storage system, both in an automatic and in a guided manual manner. To demonstrate our approach, we introduce DR4DNA, a software toolkit that contains all methods presented. We evaluate DR4DNA using both in-silico and in-vitro experiments.