Hello from the PowerPC Macs forum, I was searching the term “Dashboard” in MR and came across this thread. Glad your weather widgets are functioning again, didn’t know the problem had been fixed; I found a workaround when it happened and just haven’t looked back. Thought I’d add my solution here for posterity, in case it happens again. This fix applies to MacOS 10.11 El Capitan, but given that Dashboard hasn’t really changed, it should also work in earlier and later versions of the OS. YMMV, try at your own risk.
So here’s the deal: the Apple-supplied Weather widget from 10.5 Leopard will work in newer versions of OS X & MacOS. You just have to make sure you’re using its old javascript parser along with it.
I copied the older version of the Weather widget from a PowerBook G4 running Leopard to my MacBook Pro running El Capitan. I then replaced El Cap's javascript weather parser with the one from Leopard. The Leopard version of the widget began to work in El Cap, so I disabled the newer version and have since been using the older one without issue.
The weather parser script can be found in a Leopard install by going into the Finder’s “Go” menu and typing /System/Library/WidgetResources/.parsers/ into the "Go to Folder" box. The one you want is "weatherParser.js" - copy that from Leopard and paste it into the same place in El Capitan (or whichever version of MacOS you’re using).
PLEASE NOTE: Doing this will break the newer version of the weather widget. You can use it again, but you’ll need to have saved the weatherParser.js file you replaced, and restore it; or copy one over from a different MacOS install. The two parsers are incompatible with each other; the Leopard version pulls its data from Accuweather, while newer versions pull it from The Weather Channel. I prefer Accuweather, so this isn’t a problem for me.
There may be a way to keep and use both widgets with their respective parsers, but I didn’t look into that. I like the older version of the widget better anyway, and this fixed my problem so I didn’t investigate further.
FWIW