On every LCD you can see (more or less) that the backlight is shining through but the S1910 should have a very good black level because of its S-PVA panel. Monitors with a TN panel have a much more worse black level.
Is this your first LCD monitor? If so I could imagine that you are not accustomed to the peculiarities of LCD monitors - the shining through is one of them. You won't get a 100% black, especially not when you have turned off all lights in your room.
Maybe you should visit the next computer store and try to get a demonstration of a LCD monitor with a black screen. Also try to get a TN panel based monitor (normaly the cheap ones *g*) for this so the shock effect will be better because there you will see a really bad shine through
And I'm sure after this you will love your S1910 with its black level. But if you don't see a real difference it might be possible that your EIZO monitor is not alright.