What's wrong with the window? Can you incorporate into design? or remove and make a door way into new addition? Do you have a plan drawn up? Don't let it be a limitation, use it to your advantage!

The window is in a bedroom and is about 3 feet above floor level and also has a radiator below it. I've included a photo which shows the window from inside the bedroom. These limitations would make it difficult to convert the window opening into a doorway..If I demolish the vinyl-clad addition, I was thinking of adding the basement walkout doors to the exterior brick wall of the house ( similar to photo2) Doing this would expose the basement door, landing and stairs to the exterior elements. In order to avoid having to add a drain and sump pump @ the landing outside the basement door, I was thinking of enclosing the exposed basement door, landing and stairs inside a 2 story screened porch which would incorporate the bedroom window. The roof of the new screened porch would follow the lines of the existing roof above the bedroom window and the side walls of the porch would line up with the portion of the house that currently jogs out. This would make the porch about 15 feet wide, whereas the current vinyl-clad eyesore is only 6 feet wide and 7 feet tall. I have no idea what condition the brick wall will be when I remove the vinyl-clad addition.

Well it sounds like a good plan to me! I think it would be better to start new - who know how well the previous owner constructed the existing entrance, aka "eye sore". I doubt the brick would be any worse then the existing exposed brick - if anything it should be in better shape.
Have an architect draw up some plans, then ask a few contractors to price it out.