Remember that windows are only part of the sound equation. Are your walls insulated? Have you sealed and caulked any and all cracks? If so, your windows may be the culprits and you can go down that road. If you have enough room on the jamb, an interior storm window is another less expensive option.

Very tough to tell where the short circuit is in this case.

What is the wall cladding and system like? Is there a bunch of air leakage through the window at the operable components.

http://www.stcratings.com/

Here is a link that might be useful: STC Ratings and principles

I know that the windows are the major problem. My question is if it would be more beneficial to buy new vinyl replacements or repair the old cheap ones. The walls are not insulated and I realize that is no good, but they have a lot of mass to them. Aluminum siding over wood siding, thick one hundred+ year old 2x4s, a layer of horse hair plaster and lathe board, and then a layer of painted wood paneling. I will eventually tear that all down to insulate and drywall... But that isn't really an option at the moment!

I would repair the old ones and then replace them with the additional work on the walls. One man's opinion.

I would repair the old ones and then replace them with the additional work on the walls. One man's opinion.

If you want, try the plexi/lexan solution on one and see what the impact it.

That way you can vet the one option before proceeding to another.