This could be caused by any number of problems.
Is this for a USB wifi dongle as the screenshot above seems to suggest? I'll assume it is for now. The yellow error driver is for the Vista IPv6 driver, so "shouldn't" be causing any issues with the wifi card itself. You can disable IPv6 within the network adapter properties though if you want to make sure.
It sounds silly, but try another USB socket, see what happens then. It should detect it and go through the new hardware process, but obviously already has the driver and will install it automatically. If you have the driver CD, try uninstalling the driver and then re-installing it using the CD.
Then go to the start menu, and in "start search" type "services", and then click on the Services option that will appear (it will have a blue cog next to it). Check that services such as WLAN Config (this is the important one), Network Location Awareness, Internet Connection Sharing etc are all set to automatic, and make sure they are all started.
The driver itself is enabled and running fine from the looks of things, so we can count that out.
As you can use it via ethernet, can you connect to Windows update and see if it detects any driver updates for your wireless adapter?
Who is the manufacturer of the dongle (I know its using the Realtek chipset, but the actual manufacturer of the dongle is important to obtaining the correct driver - there is different variants of that particular chipset, never-mind the manufacturer).
You could use system restore to see if it resolves the issue, if it started only recently - you can access it by opening the start menu and using "start search" and typing "system restore" and follow the instructions to restore your system to a date before the problems started.
Do you have the box, or is there any stickers on the dongle saying a model number etc??
Try fixing any problems with the file-system, go to the start menu, in "start search" type "cmd" and command prompt should appear in the start menu... right click on it and "open as administrator". Okay the UAC prompt and type "sfc /scannow" - if it finds any errors and fixes them, great, it may solve the problem! It may need an error manually fixing, or it could find none at all.
Also, download and run Malwarebytes
and Hitman Pro
and see if they find and fix anything. Hitman Pro doesnt need to be installed, just run it.
If none of these detect anything, there is lots more tools, software and fixes you can try to resolve the issue, but we could be here all day lol. If you want me to take a look at the laptop, I can do so at no charge.
Let us know how you get on.