If your server stopped working after a Garrysmod update, or you added an addon or game mode that broke it, the first thing to try doing would be to resubmit the "Easy setup" page to refresh your SVN-based files, then restart the server and perform a Websync operation. Then, reconnect as a client.
If the server still doesn't work after this, and a game update was just released, you might have to wait a bit for your addons/gamemodes to release new versions. If you'd rather not wait, you can start over from scratch.
To start over from scratch, back up any custom files/settings, and then schedule a wipe through the "File manager" page of your control panel. After the wipe is performed, do the following:
1. Check that your server works properly as it is, by connecting to it.
2. Disconnect and make a server adjustment, such as adding a desired addon/game mode, either through FTP or the SVN tool on your "Easy setup" page. Wait for the change to fully take effect.
3. Restart the server through your "Server control" page.
4. Perform a new Websync operation through your "Websync" page.
5. Repeat from step #1. If the server doesn't work in step #1, you'll know which adjustment was the culprit.