I had been having this problems for many months, whenever I turn on my laptop running Windows XP from the hibernation or in standby mode than the all the internet or network connections disappear and will go missing, the connection icons in the Windows Task bar will also disappear and If you open up start >settings > network connections than there will be nothing present there, however when you reboot the computer than everything comes back to normal and this problem occurs every time with hibernation and sometimes with standby.
Anyway, today I decided to dig down the problem as it was very frustrating to reboot the computer and lose your work. It turned out that the problem is due to the hanging of couple of windows services to solve this without reboot take the following steps
1) Go to start > run > type services.msc and hit enter
2) A Window listing various Windows Services will open, Go to the service with name “Network Connections” right click on it to open its properties, do a Stop and than Start the service, do this at-least 3 times
3) Now go to service DHCP Client, select the properties and click on start, if its already started than restart the service
4) Next go to the Service Wireless Zero Configuration and also start it from its properties, you need to do this step only if you are using a Wireless Network Adaptor
Now open the network connections from up start >settings > network connections , refresh the window by pressing F5 a couple of times and your network connection will be back
Now, you are all set to go , your missing network connections will be back and you will be able to browse the internet and carry out other network dependent tasks
I have tested this on Windows XP, However this should be also valid for Windows Vista and 7
If there is any problem than please post in the comments section below
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