First I have heard of it ever being out of action, it has been the number for years and a friend used it only yesterday evening as a new modem was purchased due to a nice lighting bolt taking a few modems out in this area, but he needed his connection details.
I gather the 444 1 444 was and still is the Turk Telekom number and takes you to the same call centre as 444 0 375; but more numbers the merrier.
It was certainly out of action when I tried it a few days ago. The call was answered but then the automated message was terminated half way through. After 6 failed attempts over 2 days I decided to opt for the 444 1 444 which as you say is the Turk Telekom original call center - the same one that 0375 lands at.
Interestingly enough the 444 1 444 number is now the one published on TTNet's website for contacting them so they seem to be directing as many calls to the one number.