So the hardware seems to be a standard Samsung platform. You could use just any recent kernel and select ARCH_S3C2410 in configuration to make it work. Have you managed to get root access? Probably yes, as you are reading /etc/shadow

If so, then just try to dump and examine the contents of mtd0 and mtd1 to get an idea of what kind of kernel image your bootloader expects and flash an appropriate replacement to mtd1.
However, I would strongly advise to get serial/telnet access to the bootloader before replacing the kernel/rootfs and JTAG before touching the bootloader itself.
Upd: Also note the fact that unpatched upstream kernels do not support YAFFS2, so you would need to take care about your root FS as well.