Well, it was worth a try. I thought it was maybe through the fault of a deprecated API system that Weather Underground phased out that killed its functionality (I see no reason for the parser to break if given the same provider), so I got a new API key, plus a new API address, and slotted those in where the widget kept them.
However, I'm not familiar with Yahoo! Widgets enough to try to go deeper in a bid to fix this security roadblock, however, I suspect it's just a matter of flipping some switch somewhere that tells it to not verify widgets for security, or some kind of process like that.
If anyone else wishes to take up the rest of this fix, here is the API information I used with additional data where applicable.