The screen was part screensaver, part book text and part random lines.
I contacted Amazon Customer Service via their 'live chat' system (which is really good, btw) and they told me straight out that since resetting the Kindle had not worked, it was stuffed.
I got a nice discount on a refurbished Paperwhite ($40 US off) and took the opportunity to upgrade to a version that has the 3G functionality as well; my original keyboard Kindle had only wifi which was sometimes a PITA with things like hotel wifi systems. Given that I bought the 'dead' one on Trade Me (still pretty new, but not direct from Amazon) I was impressed at the way they dealt with this. Many NZ companies could learn a lot from US companies when it comes to customer service and returns policies, I must say.
So if yours dies (and the screen thing seems fairly common looking through online postings) it is well worth contacting Amazon even well after the 12 month warranty. There is also now a 2 year extended warranty but sadly that is only available to customers in the USA for some reason.