How do I prevent water from leaking into my basement?
Call Mike Holmes.  But seriously, he had a great show in which he has a very similar problem - we are talking 8 foot by 3' trenches around entire basement, waterproof cladding, rock, dirt barrier cloth and back fill.

In a nut shell - your attempt to get the water away from those exterior walls is a step in the right direction.  Unfortunately, there may be so much water in the surrounding soil that the water content in the soil with put too much hydrostatic pressure upon the basement walls - leaky leaky. 

Is this a finished basement - flooring, drywall etc?  Worked on one basement in which a trench was put in the floor and drained to a sump pump.  A waterproof floor was elevated over the concrete and the rooms finished - It was fine 10 years later.  That said, I would not do that now as a general contractor - only the trench, seal, drain and back fill method.