That's a strange situation but if you want to download a different one and see if it helps then log into Google Market on the pc and install the keyboard from the market.. It should install without any interaction from phone.
Going to the market to download a new keyboard shouldn't need you to type in the words. You can just go to top Apps and scroll down until you find a suitable keyboard app for you.
These are all great suggestions! Thank you!
Beyond the Market apps having great potential, I would recommend placing the phone into Safe Mode, then testing the keyboard capabilities. If you do not have the issue, you know its a software related concern and you should move on to performing a Hard Reset. Just ensure you have your Google/Gmail credentials to sign in once you've completed the on-screen activation set-up.
Please advise here if this was able to resolve the issue!