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Keyboard issues are routinely symptomatic of moisture problems in the keyboard. You should first remove the battery and do your best to allow it to dry: Got Your BlackBerry Wet? - BlackBerryFAQ
You can access you Address Book by using the Address Book icon, or homescreen shortcut A: Home Screen Shortcuts - BlackBerryFAQ
You can still backup your device with Desktop Manager to restore your contacts to a new device should you end up doing that, as well as syncing your contacts to outlook.