Unable to move clips on Timeline

Hi there!

Before trying to reset your preferences, please go to Edit > Preferences > General, uncheck the GPU-accelerated UI rendering option, and restart the app. Please also share your current Premiere Pro version.

When Premiere Pro behaves oddly resetting it´s preferences often solve the issue!

1.  Close Premiere Pro.
2.  Hold down the Alt-key while you launch Premiere Pro.
3.  In the Reset options dialog, make sure that Reset app preferences are checked.
4.  Click on Continue.
5.  Open the project you are working on.

Any progress now?

Do you have the tracks locked in the Header Control block? You didn't show that, so no way we can do anything but guess.