Hi Jonas,
Web Application Project support is built-in with SP1 - so you don't need to install anything separate.
I helped someone else with a similar problem before, and it turned out the at the problem was that SP1 hadn't successfully installed. Can you try this to see whether SP1 is working:
-- Pick the File->New Project menu item and see if there is a web application project template in it. If so, pick it and see if the project opens.
If the above step doesn't work, then I suspect SP1 wasn't successfully installed on the machine. If the above step does work, then we have something else going on. Let me know how it goes and we can figure out next steps from there.
Thanks,
Scott