(The following is true if you’re using a fairly recent version of Windows:)
If you go to Start -> Control Panel -> All Control Panel Items -> Notification Area Icons
There’s a list of icons, (including the power icon) each with a dropdown box with an option for “Show Icon and Notifications” which, when selected, should return your power icon.
(Easier would be right-clicking near the clock and selecting “properties,” then clicking the correct checkbox, but I gather that’s not working for you.)
Re: the language bar icon, if you use the keyboard shortcut of alt-shift, the language bar should appear floating on your desktop. Minimize it to return it to the icon area of your taskbar.