Jay, if it were my house I would remove the old siding, address any insulation issues, install house wrap and seal any places for air infiltration, then install new siding. But thats just me. You could go over the existing, but you won't have a smooth surface to cover and you will probally build out past the window trim. Its your house, my
Be sure to go to the James Hardy web site and download their installation specs.
And Jay, welcome to House Repair Talk.