It looks like your computer is a laptop and your only network connection is wifi, is that right? Is there a built-in wifi adapter? Are you using a wifi dongle (adapter that plugs into a USB port)?
On your screen shot, the window shows you connected but the tray icon says no. You could just hide the useless tray icon, but the issue is that you want a tray icon that correctly shows the connection status?
When you are actually connected, hover over the tray icon; does it display any information (you would normally see the name of the network if that icon is for the connection)? If you see the network name but the icon shows the symbol for no connection, the problem is some form of corruption (or pranking), where the wrong icon has been associated with connected status. You might be able to fix that by running SFC /SCANNOW from the start menu Run window (it repairs corrupted system files). Actually, it wouldn't hurt to do that anyway because it may clean up other types of corruption that could underlie the problem.
If you don't see any information when you hover over the icon, right click on the tray icon and select the Network and Sharing Center. The middle of that window should show your current connections. Does your network connection appear there? It should if you are connected and that will confirm that the issue is limited to the tray icon. Click on the listed wireless connection, and then Properties. You will see a box titled "Connect Using". What does it show in that box?
Open the Device Manager (many ways to get there, such as the System window from the Control Panel). In the Device Manager, you will see a list of device categories. Expand the Network Adapters category by clicking on the arrowhead in front of it. How many adapters are listed? What are their names? Do any of them have a little yellow fault flag? (If you are able to connect, I wouldn't expect it, but it is possible to be corrupted in a way where the issue is limited to non-critical internal handshaking.)
Let me know the answers to these questions to figure out the next step.