Tracking and acquiring simultaneous optical images of randomly moving targets obscured by scattering media remains a challenging problem of importance to many applications that require precise object localization and identification. In this work we develop an end-to-end neuromorphic optical engineering and computational approach to demonstrate how to track and image normally invisible objects by combining an event detecting camera with a multistage neuromorphic deep learning strategy. Photons emerging from dense scattering media are detected by the event camera and converted to pixel-wise asynchronized spike trains - a first step in isolating object-specific information from the dominant uninformative background. Spiking data is fed into a deep spiking neural network (SNN) engine where object tracking and image reconstruction are performed by two separate yet interconnected modules running in parallel in discrete time steps over the event duration. Through benchtop experiments we demonstrate tracking and imaging randomly moving objects in dense turbid media as well as image reconstruction of spatially stationary but optically dynamic objects. Standardized character sets serve as representative proxies for geometrically complex objects, underscoring the method's generality. The results highlight the advantages of a fully neuromorphic approach in meeting a major imaging technology with high computational efficiency and low power consumption.