I've had this problem installing other GOG games. Once I found a forum thread on how to fix it, but now I can't remember. I'm using Windows 7 with Avast antivirus if it's any help.

Basically, I launch the file (UAC off, run as Admin), and the integrity check works fine, but then the installation stalls. The task manager shows that it's not responding, and there are two instances of "setup_jagged_alliance_2" in the process list. I thought it might just be a slow load time, but I left it for 2 hours and it was still the same.

Any advice?

As I recall, Avast has the very annoying wish to run any program it doesn't know/like in a sandbox environment, thus preventing any setup from doing its job. See if whitelisting setup_jagged_alliance_2.exe in Avast will fix your problem, or alternatively, fully disconnect from the internet and turn Avast off. Hope this helps, and remember to install outside of Program Files.