I take it you are using VS2005 or 2008 if you are using an app_code folder? I suspect you may need to change your publish settings. Also you said web application not website, so just in case, you cannot use app_code in web application projects only web sites, and you need to create the app_code folder by right clicking the project select add ASP.NET folder and choosing app_code from the list.
Anyway, so right click the web application select properties and go to the MSBuildOptions Tab. If you want to be able to change files individually without replacing all the assemblies in the bin folder select "allow this precompiled site to be updatable". If you decide that you want the site to be totally precompiled don't select this checkbox, but remember the asp pages will be just stubs and user controls will be compiled into an assembly. Next I suggest you choose a folder where you want to publish the compiled site too, Visual Studio sets the project folder by default. Once you have done this click apply.
Next you need to right click the web application and click publish, visual studio will then compile the project and publish it to the folder you selected.
At this stage it's probably safer to delete what you have on the web server and replace it with what you have in the new folder. I would also check that your web site is set up correctly in IIS, if this …