@Jose Alberto:I also have a Web Service and a simple Apache Cordova App running and no Problems with $.ajax calls at all. Are you sure that your request header is right? Does you Web Service require any authorization? Are you making https calls? What kind of Errors do you get?
I have a Problem running the sample Project from the codeplex site.
Every time I start the application I get the following error
System.Windows.Markup.XamlParseException: The type 'Pushpin' was not found. [Line: 45 Position: 163] at MS.Internal.XcpImports.CreateFromXaml(UnmanagedMemoryStream stream, String sourceAssemblyName, Boolean createNamescope, Boolean requireDefaultNamespace, Boolean allowEventHandlers, String xamlResourceUriString)
This happens with both sample Projects.
I downloaded the sources from the link mentioned above.