I have run into this with my Dell Inspiron Mini as well. Exact same symptoms. It took me some time but i SOLVED it out..!
Actually the F2 key (in some models Fn+F2) does not turn the wireless radio on and off by itself. Instead this key combination is there to bring up a tiny piece Dell Utility software called WSED.EXE which should have already been started up at the start up and running in the background.
Under normal operation WSED.EXE is a Dell Utiliy Software which displays an icon in the tray when running and pops up a window when pressed to the F2 key (in some models Fn+F2) or when double clicked on it's icon at the tray. Once you have it's window opened up there you will see the check boxes to enable the wireless modem and the bluetooth. (provided they had been enabled at the BIOS settings Advanced>Wireless) Just put a check on the wireless modem and you are done. If it doesn't show your wireless modem then go to your BIOS at boot by presssing F2 and simply eneable the wireless modem. (BIOS settings Advanced>Wireless)
Solution: In my case this WSED.EXE was not listed in the startup programs hence it was not running in the background at all. In my Windows 7 home edition this program is located at
c:\program files\wsed\wsed.exe.
When i run it manually it's icon (something pink) showed up in the tray and F2 key started working as explained above. I could turn the wireless raido on. Then in order to have that application to start automatically everytime i switch on the netbook i added it to the list of startup programs and everything returned back into normal as day one.
I hope this solves your problem.