That is very weird! We haven't seen this before :-/
There are similar state folders, located at:
%LOCALAPPDATA%\rstudio
%APPDATA%\Roaming\RStudio
Does deleting either of these make a difference?
If you open the Task Manager, does it show the RStudio process as hanging? Is it stuck at 100% CPU, or just doing nothing?
Do you have any better luck with the daily builds of RStudio? (seems unlikely, but worth a try)