Guys and gals, I had this same problem, I went thru all of the suggestions above, all to no avail !! I found out that, once all connections are good, all I had to do was disable the Local Area Connection and then enable it (no wireless on this PC). This refreshed the icon and all is well. The exact same process should work for you. As long as a network device is not in use and is disabled, it should not effect this icon.
Bottom line: if you use wireless, make sure any others you don't use are disabled. If you use the "Local Area Connection", make sure any others you don't use are disabled. Then, disable then re-enable the connection that you DO use. To configure your connection and refresh the icon::
1. right-click on the systray "Network" icon with the red X
2. left-click on "Open Network and Sharing Center"
3. left-click on "Change adapter settings"
4. only ONE connection should be enabled and others disabled
a. If you use wireless, you should see the word "disabled" under the "Local Area
Connection". If not disabled and you do NOT use a direct cable plugged into the LAN
connector, disable it as follows:
1) right-click on "Local Area Connection"
2) left click on "disable"
b. If you use a Wireless Network Connection", disable then re-enable it as follows:
1) right-click on "Wireless Network Connection"
2) left click on "disable"
3) right-click on "Wireless Network Connection"
4) left-click on "enable"
NOTE: you'll need to reconnect to your network if it isn't an automatic connection
5) The red X on the Network icon in the systray should now be gone.
6) skip down to step 5..
c. If you use only the cabled LAN connection, disable then re-enable it as follows:
1) right-click on "Local Area Connection"
2) if it is already disabled, skip down to step (5
3) left click on "disable"
4) right-click on "Local Area Connection"
5) left click on "enable"
5. You should repeat the above applicable procedure as necessary to disable all unused connections shown in the network connections list viewed in step 4. above.
6. After connection is re-established and IP address obtained, the red X on the systray "Network" icon should be gone.
If this doesn't resolve your issue, I would ask Microsoft. You know how helpful they'll be ? Not very b/c they are the ones that should have had this icon refresh every time you reboot (and if they do, it's BEFORE DHCP is completed instead of after). Also, the guy or gal you talk with won't be the one that wrote that particular module of Vista or 7 (since it likely wasn't done in Pakistan anyway). Not only that but you can rest assured that they will be in CYA mode for Microsoft at the threat of becoming a part of the "just over 9% statistic" reported monthly.
Good luck !!