You shouldn't reinstall in the case of a failed-to-connect message when connecting, unless you've ruled out everything else.
Looking at the timestamp, it looks like there were server outages at that point. And now you've gone and broken your client....
uninstall RO completely and delete the RO folder. Then run the RO installer - be aware that it may take an unreasonably long time to start (blame microsoft, it's windows scanning it, and the inherrently inefficient microsoft installer system). If you're using Windows 7 or Windows Vista, on the first (or was it second?) screen of the installation, choose to install it to a location outside of program files (create new "C:/games" folder or whatever - it should be installed to someplace that windows doesn't consider "special" like program files).
See if it works at that point.
If not:
Ensure that you are not running any vpn software like Hamachi/LogMeIn (that program in particular is known to prevent RO from connecting, and similar programs probably could as well).
Ensure that any software firewalls are configured to allow RO to access the internet. Be aware that after a patch that updates the client, you may have to re-allow RO, because some software firewalls detect that the program has changed, and will block it until you allow it again.
Edited by DrAzzy, 08 September 2011 - 07:23 PM.