Would appear things are almost there. You have an Intel on-board sound card and the module appears to be installed.
Actually, the correct command would be (as root)...
Are you in GNOME or KDE? Sometimes sound daemons can get in the way of things, so I recommend going back to the command line.
Don't know much about Fedora, but do you have "alsaconf"? Could try typing "alsaconf" as root.
Also, some obvious things, check your mixer settings. Make sure the volume control is actually turned up
The command is "alsamixer".
If you're trying to get sound out of apps that were designed for older OSS drivers, then you'll also need OSS compatibility modules installed.
See the Wiki article...
Keep at it