The books from the ConnStore (ConnTexts as I like to call them) aren't tied to your Reader
, they're tied to your account
. Your Reader is also
tied to your account, which is what lets you read the books.
If you get a replacement Reader from them all you'll need to do is authorize the replacement to your same account and all your ConnTexts will become usable on the new Reader.
If you can get it to let you do so (and if it really is just the display as you suspect, it probably will let you), I'd suggest you de-authorize your current
device from your account before you send it back to them, that way it won't be taking up one of your six permitted slots, and you won't have to call them to have it removed from your account.