Sign into I-tunes

How can I sign into I-Tunes. I entered the correct name and password and the system keeps coming back with the same sign in prompt. If use an incorrect password the system prompt does come back with the comment that I have used the wrong password.

I then created a new password, which was accepted by the Apple system, but the same thing happens, with the same sign in prompt coming back repeatedly, but without any indication if anything is wrong.