I'm trying to download the Redneck Rampage soundtracks,but the downloads not starting.

Are you trying to download using the downloader or your browser? Whichever, try downloading with the other one. Also make sure you don't have any 3rd party download managers running at the time as they can cause problems.

You can't download the soundtracks with GOG downloader.

What browser (including version) are you using? Are you able to download files from other websites? Are you running any kind of firewall or NAT router?

So do you have any download manager plugins installed? Those can conflict with certain servers' policies and they'll bar you from downloading the file.

Using Firefox 3.5.3 with FlashGot extension and IDM .Downloaded the Fallout series extra content withouth any error.It worked fine with the Redneck Rampage extra content ,except the soundtracks.The downloads not starting.
IDM error HTTP/1.1 403 Forbidden

Definitely contact GOG support, that sounds like a server-side issue.

The first thing you should try is downloading using a different browser.