Gmail connectivity for users accessing email through a web browser are easy to troubleshoot.
First, be sure that you have a working Internet connection. Attempt to connect to big, well-known websites such as, google.com or cnn.com to ensure that they are loading. If not, then your problem is that your Internet connection is not working, not that you are actually having a Gmail connectivity issue.
If you can connect to other Internet websites, but cannot get Gmail to load, try accessing it by directly typing both gmail.com and mail.google.com into your web browser. Although unlikely, there is a possibility that your client is having trouble resolving the Gmail email service address. If both of these connections fail, but other Google pages, such as Google Voice can load, it is possible that either Gmail is actually down, or that you have a Gmail based virus.
If Gmail loads, but you cannot log in to your account, check to ensure that you are using the right username and password. Be sure to manually type them into the fields as your browser's Save Password feature may be having an issue. If this does not work, then you will need to follow the procedures to recover your username and password. This is why is is always a good idea to keep your alternate email address up to date on your Google Account to ensure that you can have a password reset link emailed to you.