"The sandboxed code execution request was refused because the Sandboxed Code Host Service was too busy to handle the request"
This error takes place for custom solutions, so you can still add other webparts, but not your custom sandbox webpart. This problem is usually present on the development environment because SharePoint can't check certificate revocation. The quick way to address this is to redirect the url to the local environment.
Open the host file and add this entry: (host file should be at system32/drivers/etc)
Save the host file and re-start the SharePoint 2010 User Code Host Service. You can now try to add the webpart to a page. The webpart should get added. You should now be able to also debug your webpart from Visual Studio.
Please note that this solution is only applicable for development environments. This is not recommended for production environments.