Do you know were can I find a new LCD Display?

Yes I do, https://www.gounlock.com/search.php?prod..., the teardown is fairly straight forward, take your time, when you use the link to order you will see there are 2 options for Digitizers and only one for your LCD , good luck, If this answer was helpful please remember to mark it accepted

The DX doesn't have an LCD screen. Its screen is is an electronic magnetic ink display. That's why it continues to display with no power and while off. Used screens are available, but keep in mind that they will not be guaranteed in any way and is likely to cost more than a newer ereader.