I'd agree you may want to simply do a repair installation.
If you really just lost the start menu shortcuts, however, the folders for things like Accessories and Administrative tools are in the folder at:
(e.g., C:\ProgramData\Microsoft\Windows\Start Menu\Programs\Accessories)
... and the relevant programs then simply have shortcuts placed in those folders.
The calculator, for example, is a shortcut to:
The character map is in:
C:\ProgramData\Microsoft\Windows\Start Menu\Programs\Accessories\System Tools
and has a shortcut to:
The administrative tools don't look like they'd be quite as easy to reassemble though, especially given their separate menu and presence in the control panel.
If it was me, I'd back up anything critical and try the repair install.