Hello and welcome to the forum.
There are no easy, elegant ways to "find programs when the start menu fails to work"
For the most part Win32 Applications will be in C:\Programs Files or C:\Program Files (x86) but that is a pretty clumsy way of having to go about things.
Maybe getting your start button to work might be a better approach, so.....
Without knowing much about what you can actually do or where you can do it from, try.....
Going here
C:\Windows\System32 and find ....
cmd.exe (if you're hiding file extensions, it'll just say cmd)
Right click it and choose Run as Administrator and then.....
In the command prompt window type
net user JohnSmith /add
hit enter
then type
net localgroup administrators JohnSmith /add
hit enter
type
exit
hit enter
Restart and log in as JohnSmith
See if the Start Button / Menu works with the new user profile.
If so then the problem is likely unique to your profile.