The sidewalk going around my house was poured very close to the edge of the basement window. The slab has sunk and water no pools against the house in that area. If we get a torrential rainfall, the water will pool up and over the wind ledge and then starts to seep through the old window onto the window sill in the basement. The sill is only about 1.5" up from the sidewalk. Any thoughts on how to stop the water from flowing through the screen? I know the simple answer would be to fix the grade of the cement, but right now I can't find a company that can help for various reasons. So I am trying to at least find a solution to the window ledge until I can find a long-term solution. Any help please!
One possible solution would be to get a clear plexiglass panel, cut it to size and seal it on the window. You can either build a "dam" blocking the lower half of the window, or seal the whole surface and make it waterproof. Of course, air flow in this case will be completely blocked, which may be a problem (and in some jurisdictions, illegal - where I live for example you can't block airflow to a room with a gas heater, or install a gas heater in a room without the mandated airways).
There are also special magnetic seals so that you can glue one of them on a cut-to-measure plexiglass window, and caulk the other half all around the inside of the window niche. They make a good seal and pressure will be a few inches of water at most. That way, you can have a real window most of the time, and just batten down the hatches when the rain comes.
Another possibility, since you are going to re-grade the concrete sidewalk anyway, is to drill a transversal draining groove from next to the window to the border of the sidewalk, so that the water is drained from your windowsill into the street. This won't work if there's a high risk of the "channel" getting clogged by dirt and debris, e.g. pine needles, dust, or moss.
Short term solution: use solid concrete blocks and polyurethane caulk (like you have between the sidewalk and house.) to build a dam in front of the window. Blocks ar available in various sizes and you could use some 8" ones on edge to build an 8" dam if you think it needs to be that tall.
Long term solution: remove part of the sidewalk and install a drain that diverts the water elsewhere.