There can be an only reason to have WinEdt not showing its "TeX" menu without manual customizations: you have accidentally switched configuration...
To overcome this problem, go to "Options" -> "Configurations" menu and click "Default (Auto-Detect)". Everything will be back again.
A little explanation
WinEdt can be used for different purposes other than TeX editing.
Excerpt from the documentation:
WinEdt is used as a front-end for compilers and typesetting systems, such as TeX, HTML or NSIS.
From the "Options" -> "Configurations" menu you can choose what to use WinEdt for.
Choosing "Default (Auto-Detect)", WinEdt will detect your installed TeX distribution and you can use it for all the mentioned tasks.