Your first widget has the magic word WordPress in the description, so I would have backed away.
Your second one uses php. So that's causing your problem.
You say " I can not run PHP/ASP on this website." Maybe time to look for another site. Plenty of free ones out there that allow php or asp.
I use firefox with Speed Dial and one of the sites is http://www.weather.gov/
set to my little town. There are a number of weather sites that you can open in a browser and a number of widgets that displays weather on your desk top. I got one with vista.