I want to change the normal Unity splash screen to be customized for my game and every time I change the splash image in the player setting it does not appear. So how can I do that please?
There is no splash screen built in for Unity standalone PC/Mac builds. You can change the banner on the config dialog. (See here http://unity3d.com/support/documentation/Components/class-PlayerSettings.html).
If you want a splash screen when the game starts after the config dialog happens you'll have to do it yourself. It's pretty easy, just put the image on a quad and make the camera so it sees the whole thing. You can do fading in/out with lerping the shader color over time, or something similar to that.
I'm assuming you don't have unity pro?
If you want custom splash screens for IOS you also need IOS pro.
Check out the licenses page: http://unity3d.com/unity/licenses