Strange. I loaded your theme and it worked fine.
The important note in the log is "LH_WeatherConnector: Error during HTTP fetch: "Request aborted"" That strongly suggests your machine is unable (for some reason) to access the yahoo weather servers.
I've put together a debug build which will spit out some more info to the debug log. Please replacew your current lh_weather .dll with this one and let me know what it spits out into the log when you lead it.
If everything was working you'd see this:
LH_WeatherConnector: Fetch WOEID for: "Nuuk, Greenland" via "http://where.yahooapis.com/v1/places.q('Nuuk,-Greenland')?appid=itP1aXDV34FW8OAAepdI2XJOKWWqJRUvV0NC_QaGlLwTryEZGw228CtxtzzYv9wceq73jDvqTYFhhA--"
LH_WeatherConnector: WOEID acquired: "472856" BEGIN FETCH (2Day)
LH_WeatherConnector: Fetch 2Day via "http://weather.yahooapis.com/forecastrss?w=472856&u=c"
LH_WeatherConnector: Fetch 5Day via "http://xml.weather.yahoo.com/forecastrss/GLXX0003_c.xml"
If it isn't working though, try opening those links in your browser and see what you get. I don't know what firefox does with RSS feeds, sp try opening them in IE (I know, I know, it hurts, but do it anyway; this way I know exactly what to expect if the feeds load correctly). The first one should appear as raw XML (there's no nice html formatting for this one as it's only meant for applications). This is probably the best test for whether you can get to the yahoo servers, but open the other two as well. One should be a very boring weather page for Nuuk, the other a similar page for Godthab (where the nearest actual weather station really is)
Let me know what happens.
I started by uninstalling LCD, delete the folders. Then reinstall it and the weather-app, then add the debug-file.
When opening the links manually, i get the right info.
(Nuuk = Greenlandish word, Godthaab (Old danish) = Danish word, for the same town. Wierd they use both to confuse though.

)
(Just to sum it up).
Generally, "Chill: factor", "City", "Humidity", "Wind", "Sun up/down", "Visibility" shows as intended.
Though "Temperatur", "Current..Description" and the weather-images don't always show.
And "Forecast Day 1+2", come once in a fullmoon, "Forecast Day 3+4" i have yeth to se.
..
Here is the Log: ( i changed the updater to 1 min).
06-11-2010 15:13:38 DBG LH_WeatherConnector: Fetch WOEID for: "Nuuk, Greenland" via "
http://where.yahooapis.com/v1/places.q('Nuuk,-Greenland')?appid=itP1aXDV34FW8OAAepdI2XJOKWWqJRUvV0NC_QaGlLwTryEZGw228CtxtzzYv9wceq73jDvqTYFhhA--"
06-11-2010 15:13:38 DBG LH_WeatherConnector: Units Changed: Update Weather (2Day)
06-11-2010 15:13:38 DBG LH_WeatherConnector: Fetch 2Day via "
http://weather.yahooapis.com/forecastrss?w=472856&u=c"
06-11-2010 15:13:39 DBG LH_WeatherConnector: Fetch 5Day via "
http://xml.weather.yahoo.com/forecastrss/GLXX0003_c.xml"
06-11-2010 15:13:39 WRN LH_WeatherConnector: XML ERROR (2Day Parser): 1 : "Start tag expected."
06-11-2010 15:13:39 WRN LH_WeatherConnector: Error during HTTP (2Day) fetch: "Request aborted"
06-11-2010 15:13:39 DBG LH_WeatherConnector: WOEID acquired: "472856" BEGIN FETCH (2Day)
06-11-2010 15:13:39 DBG LH_WeatherConnector: Fetch 2Day via "
http://weather.yahooapis.com/forecastrss?w=472856&u=c"
06-11-2010 15:13:39 WRN LH_WeatherConnector: XML ERROR (5Day Parser): 1 : "Start tag expected."
06-11-2010 15:13:39 WRN LH_WeatherConnector: Error during HTTP (5Day) fetch: "Request aborted"
06-11-2010 15:13:39 DBG LH_WeatherConnector: Fetch 5Day via "
http://xml.weather.yahoo.com/forecastrss/GLXX0003_c.xml"
06-11-2010 15:13:39 WRN LH_WeatherConnector: XML ERROR (2Day Parser): 1 : "Start tag expected."
06-11-2010 15:13:39 WRN LH_WeatherConnector: Error during HTTP (2Day) fetch: "Request aborted"
06-11-2010 15:13:39 WRN LH_WeatherConnector: XML ERROR (5Day Parser): 1 : "Start tag expected."
06-11-2010 15:13:39 WRN LH_WeatherConnector: Error during HTTP (5Day) fetch: "Request aborted"
06-11-2010 15:13:40 DBG LH_Lua: "Cairo version 1.10.0"
06-11-2010 15:13:40 DBG LH_Lua: loaded SamplesLuaCairoTest from "lua/cairotest.lua"
06-11-2010 15:14:39 DBG LH_WeatherConnector: Update Weather (2Day)
06-11-2010 15:14:39 DBG LH_WeatherConnector: Fetch 2Day via "
http://weather.yahooapis.com/forecastrss?w=472856&u=c"
06-11-2010 15:14:40 DBG LH_WeatherConnector: Fetch 5Day via "
http://xml.weather.yahoo.com/forecastrss/GLXX0003_c.xml"
06-11-2010 15:14:40 WRN LH_WeatherConnector: XML ERROR (2Day Parser): 1 : "Start tag expected."
06-11-2010 15:14:40 WRN LH_WeatherConnector: Error during HTTP (2Day) fetch: "Request aborted"
06-11-2010 15:14:40 WRN LH_WeatherConnector: XML ERROR (5Day Parser): 1 : "Start tag expected."
06-11-2010 15:14:40 WRN LH_WeatherConnector: Error during HTTP (5Day) fetch: "Request aborted"
06-11-2010 15:15:41 DBG LH_WeatherConnector: Update Weather (2Day)
06-11-2010 15:15:41 DBG LH_WeatherConnector: Fetch 2Day via "
http://weather.yahooapis.com/forecastrss?w=472856&u=c"
06-11-2010 15:15:41 DBG LH_WeatherConnector: Fetch 5Day via "
http://xml.weather.yahoo.com/forecastrss/GLXX0003_c.xml"
06-11-2010 15:15:41 WRN LH_WeatherConnector: XML ERROR (2Day Parser): 1 : "Start tag expected."
06-11-2010 15:15:41 WRN LH_WeatherConnector: Error during HTTP (2Day) fetch: "Request aborted"
06-11-2010 15:15:42 WRN LH_WeatherConnector: XML ERROR (5Day Parser): 1 : "Start tag expected."
06-11-2010 15:15:42 WRN LH_WeatherConnector: Error during HTTP (5Day) fetch: "Request aborted"
Also.. Tried disabling my firewall, with the same result.