Is it only T? Does pressing N open a new window, and does R reload the page?

The most likely reason for this is that the CTRL key is held down - see Keyboard shortcuts - Perform common Firefox tasks quickly for information on what should happen when keys are held down together.

If a key isn't stuck or being held down, an extension could be the cause. See Troubleshoot extensions, themes and hardware acceleration issues to solve common Firefox problems to troubleshoot.

You can try to press all the status keys (Shift,Ctrl, Alt) on the left and right side of the keyboard a few times to see if that helps.