I am working in ArcMap 10.2.2. I am trying to project a NED 3m dataset from a Geographic Coordinate System to a Projected Coordinate System. The output rasters pixels do not overlap the original rasters. I have used the snap to raster in Environments, both with the Background processing enabled and not. I have tried running the projection in ArcCatolog and Arcmap. Does anyone have any idea how to align these rasters.
You will not be able to align these rasters in different coordinate systems especially since they are built from different datum. In the screen capture here, I have taken a raster with UTM projected coordinates and reprojected to GCS WGS 84. You can see the difference in linear shift of the corner of roughly 60m. Unless all of your rasters are projected in the same system, there's no way to guarantee registration between cells.
Are the raster pixel sizes the same? If one is 3m and the other is 10m then there is no way that they can correctly overlap. I would look into that first. Second, if there is a common raster that you can clip it to outside of the ones you are using that shares that same cell size, then I would use that. Double check on the cell sizes to make sure that there aren't any discrepancies. The coordinate system change may cause some shifting as well, depending on which systems you are using. I would try to change the coordinate system within ArcCatalog by right clicking the layer, and then going to properties, and changing the system from the geographic coordinate system to the projected coordinate system. Then reload the data into the map.