I've had this problem happen to me with a few wireless keyboards. Sometimes you have to "start from scratch" as it were, by unplugging the RF USB unit and then reboot your PC, THEN plug in the RF unti again, wait until windows finds it, then go through the process of connecting the mouse & keyboard. Unfortunately, I've also had a few of these keyboards decide to die the same time the batteries died and needed replacing. If you are absolutely sure that the batteries are fresh and are working, but can't get the keyboard to connect and work, you have a dead keyboard I'm afraid. :-(
Always keep your receipt for these things, even though they are dirt cheap, like £15, they do have a 1 year warranty from Argos so you can take them back for a replacement. I did that just today as my Logitech Wireless Keyboard died last night, and as I had bought it in May and still had the receipt, (which totally surprised me as I never keep receipts for stuff that cheap) I exchanged it at Argos for this keyboard mentioned in this topic.
Alex Devlin, August 2010