We have searched for weak fast radio burst (FRB) events using a database containing 568,736,756 transient events detected using the Parkes radio telescope between 1997 and 2001. In order to classify these pulses, and to identify likely FRB candidates, we used a machine learning algorithm based on ResNet. We identified 81 new candidate FRBs and provide details of their positions, event times, and dispersion measures. These events were detected in only one beam of the Parkes multibeam receiver. We used a relatively low S/N cutoff threshold when selecting these bursts and some have dispersion measures only slightly exceeding the expected Galactic contribution. We therefore present these candidate FRBs as a guide for follow-up observations in the search for repeating FRBs.