Thank you for your answers and for the bug report.
Looks like the reason for the issue is related to the code editor that is used for Visualforce pages. We continue looking for a reason.
Right now, as a workaround, please follow the next steps to get an ability to work on Visualforce pages:
1) please right click on the necessary page file in the Solution Explorer;
2) select the 'Open With... item';
3) choose the 'XML (Text) Editor' and 'Ok'.
This can be a temporary solution till we are working on the issue.
Also, I kindly ask you to help us in our investigation the next way: please close a solution in the IDE (if any), open File (in the main menu) -> Open -> File, and select any your Visualforce page file from a project. Please let me know if the issue would be reproduced in this case.
One more possible solution could be to re-install Microsoft Visual Studio 2013 Isolated Shell.
If this is acceptable for you, you can do the next:
1) please uninstall Microsoft Visual Studio Shell (Isolated);
2) after this please uninstall The welkin Suite IDE;
3) download Microsoft Visual Studio 2013 Shell (Isolated) using the next link and install it separately from the IDE;
4) re-download TWS from the site and install it again;
5) repeat the workaround that helped you to log in;
6) and launch the IDE.
After this please check again if the issue would be reproduced.
Thank you for your collaboration one more time!
Looking forward to your response.