Iphoto will not open

You need to clarify here.

Usually when I back up with Time Machine they reappear but not this time.

Back up what? And where do they reappear?

What verion of iPhoto do you have? What happens when you try to open it?

When I use Time machine for a full system backup and they reappear in Iphoto.

Backing up won't cause anything to reappear. Restoring from a back up might. Is that what you mean?

The words "Iphoto" appears in Menu Bar but nothing else happens.

Try trash the com.apple.iPhoto.plist file from the HD/Users/ Your Name / library / preferences folder.

(On 10.7 or later: Hold the option (or alt) key while clicking on the Go menu in Finder to access the User Library)

(Remember you'll need to reset your User options afterwards. These include minor settings like the window colour and so on. Note: If you've moved your library you'll need to point iPhoto at it again.)

What's the plist file?

For new users: Every application on your Mac has an accompanying plist file. It records certain User choices. For instance, in your favourite Word Processor it remembers your choice of Default Font, on your Web Browser is remembers things like your choice of Home Page. It even recalls what windows you had open last if your app allows you to pick up from where you left off last. The iPhoto plist file remembers things like the location of the Library, your choice of background colour, whether you are running a Referenced or Managed Library, what preferences you have for autosplitting events and so on. Trashing the plist file forces the app to generate a new one on the next launch, and this restores things to the Factory Defaults. Hence, if you've changed any of these things you'll need to reset them. If you haven't, then no bother. Trashing the plist file is Mac troubleshooting 101.

Are you asking about this?

Trashing the plist file forces the app to generate a new one on the next launch, and this restores things to the Factory Defaults.

iPhoto will create the ".plist" file again, the next time it runs, because it cannot run without such a file.

After you removed the "com.apple.iPhoto.plist" you need to log off and on again, before trying to launch iPhoto again, otherwise the changes may not take.

Launch iPhoto by double-clicking the iPhoto Library. The plist file contains the path to your iPhoto library. After removing this file, you have to point iPhoto to the location of your iPhoto library. Otherwise it will create a new, empty library.

Sorry for not understanding, but how do I point iPhoto to the location of my iPhoto library. Thanks.

You said, that you are using Iphoto 11 version 9.4.3.

This version will switch to an iPhoto library, if you select that library in the Finder and double click it.

If trashing plist will help with a Mail problem will depend on the kind of problem you are experiencing. Thrashing plist usually will help, when elements of the graphical user interface are not reacting as they should. You'd better ask a specific question in the Lion forum: Mac OS X v10.7 Lion

Describe what is wrong with your Mail, your system version, and what you already have done to solve the problem.