After selecting my text layer at the top of the layers list, when I go to grab the layer it instead activates and moves the background layer underneath it. A have to click on the text layer several times before it will actually let me select the text layer.
When you're going to grab the layer, are you clicking on the actual text? If not, the Auto-Select feature of the Move tool may be what's triggering this issue for you. By default, it's on. You can disable it when the Move tool is active -- it's the first control on the left in the Options Bar.
Hope that helps -- ping me again here if you need further assistance.