Could you please run Windows Update and check if it solve problem?
That absolutely did seem to solve it. Thank you!
I had the same problem. Windows 7 64-bit with all the latest updates and .NET 4.5. Unfortunately I got stuck just right at the start with following error (according to Event Viewer):
<Provider Name="Application Error" />
<TimeCreated SystemTime="2013-09-25T22:50:06.000000000Z" />
Nothing worked. Until I googled out 2.0.50727.5472
which was version number of files replaced with certain "Windows Update fix". KB2833946 to be exact. I've uninstalled this fix and.. GOG.com Downloader fired up without hassle.
Conclusion? GOG.com Downloader is incompatible with KB2933946 security patch and 2.0.50727.5472 .NET files. At least for me. Please check it if you can.