Hey Baksha,
The app I was referring to is just called "Amazon", and does not have the same icon as any of the installed application level apps. It is a black background with white and orange writing. I had the exact same issue you are describing, and until I stopped that app, and cleared its data and cache, I was unable to get things cleared. The exact process I went through that finally worked was:
1. Go into accounts on phone, and delete the Amazon account there
2. Disable all pre-installed Amazon apps, including Amazon Mobile, Amazon MP3, and Amazon Kindle.
3. Go into Settings -> Apps -> All
4. Force stop the afore mentioned Amazon system level app
5. Clear its data and cache
6. Now go back into the Amazon MP3 app, and re-register
7. Once this is functional again, then you can re-enable and re-update the other Amazon apps
Amazon has no idea what is actually causing the issue, and is not interested in addressing it, otherwise they would attempt to interact with the people reporting the issue. Perhaps if enough folks reported it to Motorola, they could put some serious pressure on Amazon to get things figured out.