After breaking off the rusted out screws and removing the lid, I had to drill out the rusted/broken screws from the mounting holes in the lid. I drilled them out and re-tapped them with a # 6-32 machine screw tap and bought new stainless steel socket head screws.
I had to remove the top of the washing machine as well to remove the rusted off piece of the hinge from the rotating spring mechanism that the hinges slide into, as well as to repair the rust around the bleach cup. I removed all of the rust with a wire brush and a scraper, treated the rusted area with a 50-50 mix of vinegar and water, rinsed and dried the area and re-painted it.
I reassembled all the parts and the repair works and looks great.