You should probably talk to your IT people about this.
GMail cannot connect to an Exchange server. It can access POP and IMAP accounts, I believe. If your IT department have not enabled POP and IMAP access to your Exchange account, you'll not be able to view the messages in the GMail window.
UPDATE for OP question:
Your iPhone connects because it has an Exchange client. Essentially, it has a mini-Outlook program.
There are different ways that email servers and services work, depending on the application and need. Most servers support multiple methods of communication and delivery.
The common methods for public email as POP/SMTP, and IMAP. These operate over the open internet and work well for connecting your home email program to an email server.
Domino and Exchange and email systems designed for use inside corporate networks. They are not the same as POP/SMTP and IMAP, though Domino and Exchange servers can be configured to allow POP/SMTP and IMAP connections if the administrator so desires. But you must keep in mind they are NOT the same thing. An email client that only supports POP and IMAP will not support Exchange or Domino.
Your iPhone normally connects POP and IMAP, and in order to make the device appeal to business users, Apple also produced an Exchange client that allowed connection to corporate Exchange mail servers. Gmail does not have an Exchange connector, generally speaking, because it is not designed for use in a Corporate Environment.
Now Google also has business aspirations and has offered Google Apps and other systems that function like Exchange or probably even connect to Exchange servers in a way so that users may use Google mail for their business mail. But this is not a standard part of the Gmail setup. The average Gmail user will not be able to connect their Exchange email account to their Gmail interface.