First of all, thank you very much for documenting the solution. I don't understand the problem either, but I have some observations to add.
In my case, I have two copies of the gadget running (Win 7, 32-bit). Both morphed into giving me the forecast, rather than the current weather conditions. Uninstalling one and reinstalling it produced the "Cannot connect to service" caption. The other
continued to give me the forecast.
I did diffs on the files, and the settings.ini files were identical, while the changes in the
.xml files seem trivial.
Adding the weather gadget to another user account on the same machine yielded the "Cannot connect" gadget.
I did the repair process stepwise.
I replaced the \cache\168522d5-1082-4df2-b2f6-9185c31f9472\.xml* files first, and the forecast gadget returned to normal operation after a restart. The "Cannot connect" gadget was unchanged. I don't know if the restart was necessary, or if
I was just too careful/impatient.
I next replaced the config.xml file. The "Cannot connect" gadget returned to normal operation; no restart required.
I installed another copy of the gadget for a third location, and it also worked normally. Based on that, I doubt that malformation of the
_wc-GMX*_.xml files are the problem.
Hint; I copied the files from another user account on the same machine, where the gadgets were working as expected; no second machine was required.
As a guess, the problem is related to a recent Windows update. The user account with the failing gadgets was the account in use at the time of the last automatic update, and the first account to be logged on after the update was completed and processed.
I can't reconcile that with the fact that your solution is two years old, and I just recently acquired the problem. Before that, the gadgets worked as expected on my machine (including activation on the "donor" account used in this
process).
Whatever information corruption is responsible, it must exist in the template used to generate the first gadget of an account. Subsequent incarnations extend or copy the existing configuration files.