Yep. Goto the manufacturer of your laptop, with your model number/ Product number handy, and get the latest drivers for your LAN card
EDIT.
Sorry misunderstood your question. Wifi will defiantly work if LAN is not connected. Since it's the only way to browse the web and windows defaults to it. If your laptop doesn't have a WIFI device forget about it. If you know for a fact it does well a driver issue discussed above. to find out do the following:
Windows XP
Right click on my computer and go properties
click on the hardware tab
click on device manager
Windows 7/Vista
Right click on my computer and click on device manger (left pane, second item)
If you notice any devices with a yellow Explanation mark ("!") such as "network device", or "ethernet controller" the devices drivers are not installed.
Secondly if you don't see any of those expand "network adapter" and take note of the devices, you may see two perhaps three cards listed. One is sure to be the Hardwired network card, another the wireless.