No they will not fix it under the normal warrenty... The only way Dell will deal with it is if you bought the EXTRA Accidental Damage Warrenty at an additional cost when you got your Axim.
So if you did not get this then you have 2 options basically.
You can go here and get the screen and replace it yourself. Not too hard. Others on the board have done it.
http://www.gethightech.com/Merchant2...tegory_Code=CS
Or you can send it here and they will replace the screen.
http://www.pocketpctechs.com/detail....t_ID=DX5-LCD01