The frayed area isn't on the cord itself, rather on the hard part where the somewhat cylindrical item that plugs into the computer meets the hard plastic area that tapers down to the soft part of the cord.

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I think that's the part that bibilit had in mind. This is a very common problem with these (and other similar) chargers, apparently.

What's even worse is, I think I may have killed the battery because the first week or so I had the system I accidentally pressed the PMU management button thinking it had something to do with music thanks to the logo... Now if I fiddle with it, I can get it to "see" the battery, but it says it's 0% charged and has 0hrs and 0mins to full charge...

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That's also common, especially if the battery is original to the computer (the newest of which would be at least 12 years old now).

Any way to fix this? D:

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The only way to fix your particular problem, I've found is to replace the cells in the battery, or replace the whole thing. I've had a similar problem, and I think it's due to individual cells in the battery going bad over time.
I rebuilt one of mine, and it worked well for awhile. Until I left it unused for a month or two. Back to square one...

There's also a possibility that the computer itself is the problem. For example, I couldn't get the aforementioned rebuilt battery to charge at all in a Tangerine iBook I had, but then I swapped out the logic board with another I had on hand, and it worked perfectly. A "beyond dead" battery is much more likely, though.

c