This issue occurs when the DEM has not undergone proper terrain pre-proccessing. Check to see if you have the following values and ONLY these values in your flow-direction grid: 1,2,4,8,16,32,64, & 128
If you have more than the listed values, this is your issue. In the ArcHydro toolbox, the flow direction tool uses a D8 method and as such, requires that all sinks are filled. The fact that you have more than 8 directions indicates that the flow direction tool is not working. Under the terrain pre-processing menu -> DEM Reconditioning, use the Fill Sinks tool. With the filled DEM, re-run the flow-direction tool, and then the flow-accumulation tool. This should eliminate all zeros.