Probably you have different values for your "PATH" environment variable between users.
This could happen a bunch of different ways.
Note the output.
Now right click on the menu item you said you can use, and check the properties. Somewhere in there there should be the command that gets run, and it will probably have the same path as the output from the command above.
To fix this for your user, you need to modify your shell's environment.
If you use bash, check out your ~/.bash_profile file.
In there there will be a line like...
Go ahead and add a ":" and the new path you found, close and open your terminal again, and see if you can't run konqueror.
Edit: Optionally, you could just echo your path variable as root, and copy that exact output to your .bash_profile.