After several hours of dealing with internal errors, I've finally solved the problem, so I'm passing on the knowledge to save others some time.
I bought a bricked PSP 1001 over the weekend and was able to unbrick it pretty easily. I experimented with a few different custom and official firmwares. However, after a day or so I started getting numerous internal errors (including 80082739 and 8008372A) whenever I was in the settings section. After the error I'd get a BSOD and the default settings would be restored. Also, at any text input areas (such as entering my nickname or an address on the web browser) the text would disappear or become corrupted.
This problem continued even after numerous firmware reinstalls and making sure the flash1 was formatted and repartitioned and the IDstorage keys were correct.
FINALLY, I realized it was my battery and charger causing it. I'm using a Pandora battery currently (with a normal boot loader on the MS) and some AC adapter I found laying around (not the official one or even a knock-off version). While the battery charges and functions, anytime it loses enough charge (usually around 50%), the errors begin to pop up. However, if I allow the battery to fully charge, the errors are completely gone. Needless to say I've ordered an official battery and an official knock-off brand charger.
I'm curious to know why this would cause these specific internal errors?