in one of my links you'll find an address table of the raw data partition including the offsets for the kernel.
but i doubt that your kernel got corrupted by itself. kernel, initrd and friends are read-only and I see no reason for you to deal with these things.
the kernel might become an issue by mixing non-matching firmware updates / restore sets.
the restore set does not touch the kernel. but firmware updates may do. if you apply the wrong restore set, the kernel might not be compatible.
but i guess your dictionary problems are not related to the kernel. it is more likely a permissions or file system integrity issue.
and last but not least - the stock reader software including the dictionary have bugs...
and last but not least - the dictionary is buggy
Be sure to check out the Wiki for Sony PRS-T1 Rooting and Tweaks!
Many questions are answered there already... If not - feel free to add
Some modifications will void warranty and may irreversibly destroy the device. I won't take responsibility if you damage your reader by using one of my files or following my suggestions.