The problem you're describing is very common. I've run into several people who have had the same exact thing happen. On each occasion, they contacted Amazon who shipped a new one out to them immediately--even when their warranty had expired, which tells me they're aware of the defect.
My experience with Amazon's customer service has always been top rate. My Kindle has broken two times and on each occasion they shipped a new one to me within a day and told me to send the old one back at my convenience. I wish other companies would follow their example!
You should have no problems.
Andrew E. Kaufman/Author