The entire system is highly dependent on the version/build of the Busybox it ships with (which, since this is linux, expects the Linux C library to be present).
Replacing that with a version/build of Busybox built to run on the Android C library (Bionic) --
WITHOUT also supplying the expected library ==
three things have saved you:
*) Your Kindle is dual boot and you have not (yet) trashed the alternate (Diags) system.
*) The update images that Amazon posts are complete (Main) system images.
(And our KindleTool will let you unpack that to get at the files you need for a fix).
*) All of the "HowTo" information is already posted, multiple times, enjoy yourself learning the differences between Amazon/Linux and Google/Linux (a.k.a: Android) embedded systems.
PS: First thing to do is fix your serial port interface.
There are only two ways to prevent it from having an output
*) Complete meltdown of the SoC
*) User error in making the connections (current evidence points at this cause).