Water flow over basement window sill
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.

Good luck!