Sooooo, none of this should be done by you if when you rented the house it included use of the basement. If the basement is unfinished and wasn't intended to be used that's another thing.
I would harp on the landlord until its fixed. He should be paying for both materials and labor to get it fixed right and be done with it. More slope away from the house and a french drain. When its dug up for a drain they can seal the OUTSIDE of the wall. Clean the gutters, extend the spout.
It's been my experience that once a basement leaks, nothing you can do from the inside will stop it. If water finds its way next to the wall it will get in, so keeping water away from the wall is the best option.
I am also a landlord and wouldn't dream of asking a tenant to fix something like this, that was obviously not their fault to begin with. If its really cheap rent and you want to stay you might just have to deal with water in the basement.
Patrick
