Make sure your user account is an administrator account.
Might be a waste of time but try turning the UAC off then running setup as an admin. Turn it back on after the install of course. (see image) . . . =)
Go to Control Panel, Users and turn UAC to Never notify. You might have to reboot after which you can try the install. I also suggest, if this allows an install, that you install in a directory outside of Program Files. I create one called C:\Games just for this purpose.
On the first dialog of the GOG installer (assuming this is the problem) click the Options button in the lower left corner and point the install to the new directory.
After the install, right-click the game shortcut, click Properties, click the Compatibility tab and check mark "Run this program as an administrator". You might want to add the -no3d and -doublebuffer switches as well. (see second image)
Edit: Also install any mods as an admin.
If all of the above fails, I would look at my firewall / AV / spyware programs as the probable cause. I have downloaded, with firefox, over 70 games from GOG on XP, Vista and Win 7 so I believe it is a local problem. Something about your particular setup seems to be timing out / blocking the download, possibly because it is fairly large . . . good luck . . . =)
One other thought, check available hard drive space, I have had large downloads fail if there was not enough free space for the file.