I too have a problem with the message center. After upgrading from 5.6 to 6.2.2, the message center never worked. Then I upgraded to 6.2.4, hoping that it would be fixed, but the message center still does not work. It shows "Loading Content...", but the content never loads; clicking on any of the buttons or tabs within the Message Center does nothing. It does show the little number graphic on the corner of the messages tab, indicating that there is a message, but it does not allow any other functionality. Isn't the message center part of core functionality for 6.2 and above?! I can't figure out what could have broken a piece of core functionality right out of the box with no customizations.
Can someone please help me to understand how I can reinstall or fix just the Message Center?
Please someone actually respond to this and let's find an actual fix; let's not allow this thread to be yet another dead end thread with no resolution in a long list of dead end threads in this forum.

I used firebug to investigate. Here is what I get:

Get Request:
http://localhost/DesktopModules/CoreMessaging/API/MessagingService.ashx/Inbox?afterMessageId=-1&numberOfRecords=10&__RequestVerificationToken=BjBXRJqPLqaPkPLRkBz%2Fk%2Fb7SJFZBh5oxHiT1LpfsxjFPz3uJON3vmkgSIyMsPytON%2FsWb3w9nQRqrqu6qkAD9Z2nh8aVKIEhgK993KYREBsgBd6%2F8YuoItZWQROWCwyEN5sNw%3D%3D&_=1351785053991

Response:
{"TotalConversations":2,"TotalNewThreads":1,"Conversations":[{"MessageID":3116,"PortalID":0,"To":"test","From":"SuperUser Account","Subject":"test message","Body":"testing message in message center.","ConversationId":3116,"ReplyAllAllowed":true,"SenderUserID":1,"DisplayDate":"1 day ago","KeyID":3116,"RowNumber":1,"AttachmentCount":0,"NewThreadCount":0,"ThreadCount":1,"SenderProfileUrl":"http://localhost/Admin/UserProfile/tabid/3571/userId/1/Default.aspx"},{"MessageID":14,"PortalID":0,"To":"host","From":"admin","Subject":"\u003cEnter School System Name Here\u003e Password Reminder","Body":"Dear SuperUser Account,\r\nYou have requested a Pass","ConversationId":14,"ReplyAllAllowed":true,"SenderUserID":2,"DisplayDate":"5/11/2010","KeyID":14,"RowNumber":2,"AttachmentCount":0,"NewThreadCount":1,"ThreadCount":1,"SenderProfileUrl":"http://localhost/Admin/UserProfile/tabid/3571/userId/2/Default.aspx"}]}

...so it seems the get request and response is good... but then I get an error, shown in firebug:

TypeError: $.ajax({type: "GET", url: boxPath, beforeSend: serviceFramework.setModuleHeaders, data: serviceFramework.getAntiForgeryProperty({afterMessageId: -1, numberOfRecords: pageSize}), cache: false}).done(function (messageboxView) {if (typeof messageboxView !== "undefined" && messageboxView != null && typeof messageboxView.Conversations !== "undefined") {var mappedMessages = $.map(messageboxView.Conversations, function (item) {return new messageConversationView(item);});self.messages(mappedMessages);if (typeof messageboxView.TotalConversations !== "undefined" && $.type(messageboxView.TotalConversations) === "number") {self.TotalConversations(messageboxView.TotalConversations);}if (typeof messageboxView.TotalNewThreads !== "undefined" && $.type(messageboxView.TotalNewThreads) === "number") {self.TotalNewThreads(messageboxView.TotalNewThreads);}} else {displayMessage("#dnnCoreMessaging", settings.serverErrorText, "dnnFormWarning");}}).fail(function (xhr, status) {displayMessage("#dnnCoreMessaging", settings.serverErrorWithDescription + status, "dnnFormWarning");}).always is not a function