Yard Drainage issues
Seems a little excessive to dig up the whole yard and not just add dirt.  But to find out where the gutters drain just add some food coloring into the gutter drain and see where it pops up.  It should come out a white 4 inch pipe at the curb but could be coming out a overgrown yard popup.  FYI it is illegal to drain rain runoff into a sewer line if you happen to not be able to locate the outflow someone may have done a no no.