Normally a storm drain does reenter according to model codes and has a storm trap located located prior to entering the sanitary drainage system. What your looking for not to far from this window is a trap and this could be full of debris slowing down the normal flow of storm water drainage. You can do the following.
Get some very concentrated DYE and put some down this drain and then check your main trap (if you have one) to see if this dye does indeed enter your system.
You can also hire a plumber with a water jetter and have him/her jet this line as someone listens inside your home for the jetting sounds under the slab This should also locate the storm trap if one is installed.
Hopefully some idiot didn’t just install a dry well or sump under ground and figure ground percolation would be enough.
Good luck