Hi everybody,
I was having this problem, and it was driving us crazy. Turns out it was caused by dual-monitors! I have a laptop w/ 2nd monitor at work and, this AM, I physically swapped them left-for-right. THIS is what caused revit to suddenly stop displaying the Project Browser and Properties despite the UI settings.
SOLUTION:
1) Close all programs and reset your Windows Display settings to a single monitor.
2) Once back to single-screen setup, re-open Revit and your missing panes should be there.
3) Then, WHILE Revit is open on your one screen and displaying all panes, go back to your Windows Display settings an re-enable your dual-screen setup.
4) Presto!
Three cheers to Craig, our resident Revit expert 🙂