Normally, if the text box is already selected, you need to click and drag on the border to move it. If the text box is not already selected, click and drag without letting go of the mouse button.

The default selection behaviour and protection settings can be modified via the shapesheet though so perhaps a setting there has locked the position.

If you add a new text box to the same page does it behave the same way? If it is different, you can post a sample document here so we can examine the shape attributes to work out where the problem is coming from.

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Andrew Lockton
Chrysalis Design, Melbourne Australia