I finally found a way to make Garmin Express (for Windows) work in a corporate network where you cannot access the web directly, but via a web proxy instead. This has been a discussion topic in some Garmin forums for years.
So here's how to make it work in 5 easy steps:
1. Make sure you have local Windows administrator rights. If you don't, this procedure may not work for you!
2. Install the most recent Garmin USB drivers if you have a USB connected device e.g. Forerunner 610 with ANT+ stick or a Forerunner 620 via the supplied cable.
3. download a "known to work" version of Garmin Express, e.g. http://gawisp.com/perry/garmin_uilities/GarminExpress329.exe Do not forget to check the downloaded file for viruses et cetera. Trust no one! Then start the downloaded executable.
4. Garmin Express is by default configured to autodetect proxy servers. In a corporate network where you connect via VPN, the Windows proxy settings may be misleading, and GE cannot connect to the Garmin web servers. Please be patient until the the initial splash screen appears, it takes some minutes for it to finally time out and display the "First Steps" screen.
5. Now click the "settings" icon in the top right (the gear symbol), and in the second section from above you can set the proxy settings from "Auto" to "Manual" (see screenshot below, sorry, it's in German, but you get the idea). Enter the relevant data here (name or IP address, port, and login credentials if needed.). You may have to ask your friendly network administrator for this data. Click "OK".
Done. Now you can pair your watch as usual, and you're ready to go. As a first test, create a small activity on the watch. If everything is okay, it should synchronize just fine and come up on the Garmin Connect web page.
I am not sure if this also works with any of the newer GE versions, so if you don't want to mess things up, you may want to be conservative and deactivate automatic updates (in the top box of the settings). After all, never change a running system.
This procedure worked for me using a FR610. If your machine explodes, please don't blame me ;-) ;-)
