Late to the party, but here is what I found (while stumbling on the same problem).
It seems that WPF Window requires UnmanagedCode permission.
Excerpt from Pro WPF 4.5 in C #: Windows Presentation Foundation in .NET 4.5 Matthew MacDonald.

And here's the exception stack trace when starting a WPF application deployed via ClickOnce to the Partial Trust. Note the call to the DemandUnmanagedCode SecurityHelper function from the Window constructor:
InnerException: System.Security.SecurityException Message=Request for the permission of type 'System.Security.Permissions.SecurityPermission, mscorlib, Version=4.0.0.0, Culture=neutral, PublicKeyToken=b77a5c561934e089' failed. Source=mscorlib StackTrace: at System.Security.CodeAccessSecurityEngine.Check(Object demand, StackCrawlMark& stackMark, Boolean isPermSet) at System.Security.CodeAccessSecurityEngine.Check(CodeAccessPermission cap, StackCrawlMark& stackMark) at System.Security.CodeAccessPermission.Demand() at MS.Internal.SecurityHelper.DemandUnmanagedCode() at System.Windows.Window..ctor() at WPFClickOnceDeploySample.MainWindow..ctor()
And here is the full StackTrace:
System.Reflection.TargetInvocationException was unhandled Message=Exception has been thrown by the target of an invocation. Source=mscorlib StackTrace: at System.RuntimeTypeHandle.CreateInstance(RuntimeType type, Boolean publicOnly, Boolean noCheck, Boolean& canBeCached, RuntimeMethodHandleInternal& ctor, Boolean& bNeedSecurityCheck) at System.RuntimeType.CreateInstanceSlow(Boolean publicOnly, Boolean skipCheckThis, Boolean fillCache) at System.RuntimeType.CreateInstanceDefaultCtor(Boolean publicOnly, Boolean skipVisibilityChecks, Boolean skipCheckThis, Boolean fillCache) at System.Activator.CreateInstance(Type type, Boolean nonPublic) at System.RuntimeType.CreateInstanceImpl(BindingFlags bindingAttr, Binder binder, Object[] args, CultureInfo culture, Object[] activationAttributes) at System.Activator.CreateInstance(Type type, BindingFlags bindingAttr, Binder binder, Object[] args, CultureInfo culture, Object[] activationAttributes) at System.Activator.CreateInstance(Type type, Object[] args) at CreateInstance(Type type, Object[] arguments) at System.Xaml.Schema.SafeReflectionInvoker.CreateInstance(Type type, Object[] arguments) at System.Xaml.Schema.XamlTypeInvoker.CreateInstance(Object[] arguments) at MS.Internal.Xaml.Runtime.ClrObjectRuntime.CreateInstanceWithCtor(XamlType xamlType, Object[] args) at MS.Internal.Xaml.Runtime.ClrObjectRuntime.CreateInstance(XamlType xamlType, Object[] args) at System.Xaml.XamlObjectWriter.Logic_CreateAndAssignToParentStart(ObjectWriterContext ctx) at System.Xaml.XamlObjectWriter.WriteStartMember(XamlMember property) at System.Xaml.XamlWriter.WriteNode(XamlReader reader) at System.Windows.Markup.WpfXamlLoader.TransformNodes(XamlReader xamlReader, XamlObjectWriter xamlWriter, Boolean onlyLoadOneNode, Boolean skipJournaledProperties, Boolean shouldPassLineNumberInfo, IXamlLineInfo xamlLineInfo, IXamlLineInfoConsumer xamlLineInfoConsumer, XamlContextStack``1 stack, IStyleConnector styleConnector) at System.Windows.Markup.WpfXamlLoader.Load(XamlReader xamlReader, IXamlObjectWriterFactory writerFactory, Boolean skipJournaledProperties, Object rootObject, XamlObjectWriterSettings settings, Uri baseUri) at System.Windows.Markup.WpfXamlLoader.LoadBaml(XamlReader xamlReader, Boolean skipJournaledProperties, Object rootObject, XamlAccessLevel accessLevel, Uri baseUri) at System.Windows.Markup.XamlReader.LoadBaml(Stream stream, ParserContext parserContext, Object parent, Boolean closeStream) at System.Windows.Application.LoadBamlStreamWithSyncInfo(Stream stream, ParserContext pc) at System.Windows.Application.LoadComponent(Uri resourceLocator, Boolean bSkipJournaledProperties) at System.Windows.Application.DoStartup() at System.Windows.Application.<.ctor>b__1(Object unused) at System.Windows.Threading.ExceptionWrapper.InternalRealCall(Delegate callback, Object args, Int32 numArgs) at MS.Internal.Threading.ExceptionFilterHelper.TryCatchWhen(Object source, Delegate method, Object args, Int32 numArgs, Delegate catchHandler) at System.Windows.Threading.DispatcherOperation.InvokeImpl() at System.Windows.Threading.DispatcherOperation.InvokeInSecurityContext(Object state) at System.Threading.ExecutionContext.runTryCode(Object userData) at System.Runtime.CompilerServices.RuntimeHelpers.ExecuteCodeWithGuaranteedCleanup(TryCode code, CleanupCode backoutCode, Object userData) at System.Threading.ExecutionContext.RunInternal(ExecutionContext executionContext, ContextCallback callback, Object state) at System.Threading.ExecutionContext.Run(ExecutionContext executionContext, ContextCallback callback, Object state, Boolean ignoreSyncCtx) at System.Threading.ExecutionContext.Run(ExecutionContext executionContext, ContextCallback callback, Object state) at System.Windows.Threading.DispatcherOperation.Invoke() at System.Windows.Threading.Dispatcher.ProcessQueue() at System.Windows.Threading.Dispatcher.WndProcHook(IntPtr hwnd, Int32 msg, IntPtr wParam, IntPtr lParam, Boolean& handled) at MS.Win32.HwndWrapper.WndProc(IntPtr hwnd, Int32 msg, IntPtr wParam, IntPtr lParam, Boolean& handled) at MS.Win32.HwndSubclass.DispatcherCallbackOperation(Object o) at System.Windows.Threading.ExceptionWrapper.InternalRealCall(Delegate callback, Object args, Int32 numArgs) at MS.Internal.Threading.ExceptionFilterHelper.TryCatchWhen(Object source, Delegate method, Object args, Int32 numArgs, Delegate catchHandler) at System.Windows.Threading.Dispatcher.InvokeImpl(DispatcherPriority priority, TimeSpan timeout, Delegate method, Object args, Int32 numArgs) at MS.Win32.HwndSubclass.SubclassWndProc(IntPtr hwnd, Int32 msg, IntPtr wParam, IntPtr lParam) at MS.Win32.UnsafeNativeMethods.DispatchMessage(MSG& msg) at System.Windows.Threading.Dispatcher.PushFrameImpl(DispatcherFrame frame) at System.Windows.Threading.Dispatcher.PushFrame(DispatcherFrame frame) at System.Windows.Application.RunDispatcher(Object ignore) at System.Windows.Application.RunInternal(Window window) at System.Windows.Application.Run(Window window) at System.Windows.Application.Run() at WPFClickOnceDeploySample.App.Main() at System.AppDomain._nExecuteAssembly(RuntimeAssembly assembly, String[] args) at System.AppDomain.nExecuteAssembly(RuntimeAssembly assembly, String[] args) at System.Runtime.Hosting.ManifestRunner.Run(Boolean checkAptModel) at System.Runtime.Hosting.ManifestRunner.ExecuteAsAssembly() at System.Runtime.Hosting.ApplicationActivator.CreateInstance(ActivationContext activationContext, String[] activationCustomData) at System.Runtime.Hosting.ApplicationActivator.CreateInstance(ActivationContext activationContext) at System.Activator.CreateInstance(ActivationContext activationContext) at Microsoft.VisualStudio.HostingProcess.HostProc.RunUsersAssemblyDebugInZone() at System.Threading.ThreadHelper.ThreadStart_Context(Object state) at System.Threading.ExecutionContext.runTryCode(Object userData) at System.Runtime.CompilerServices.RuntimeHelpers.ExecuteCodeWithGuaranteedCleanup(TryCode code, CleanupCode backoutCode, Object userData) at System.Threading.ExecutionContext.RunInternal(ExecutionContext executionContext, ContextCallback callback, Object state) at System.Threading.ExecutionContext.Run(ExecutionContext executionContext, ContextCallback callback, Object state, Boolean ignoreSyncCtx) at System.Threading.ExecutionContext.Run(ExecutionContext executionContext, ContextCallback callback, Object state) at System.Threading.ThreadHelper.ThreadStart() InnerException: System.Security.SecurityException Message=Request for the permission of type 'System.Security.Permissions.SecurityPermission, mscorlib, Version=4.0.0.0, Culture=neutral, PublicKeyToken=b77a5c561934e089' failed. Source=mscorlib StackTrace: at System.Security.CodeAccessSecurityEngine.Check(Object demand, StackCrawlMark& stackMark, Boolean isPermSet) at System.Security.CodeAccessSecurityEngine.Check(CodeAccessPermission cap, StackCrawlMark& stackMark) at System.Security.CodeAccessPermission.Demand() at MS.Internal.SecurityHelper.DemandUnmanagedCode() at System.Windows.Window..ctor() at WPFClickOnceDeploySample.MainWindow..ctor() InnerException: