Try specifying the full path in the launcher you are using.

So for example if the output of which matlab is /usr/bin/matlab, then change
the Exec field to

Exec=/usr/bin/matlab -desktop

Note that if this does solve the issue for you it's likely because you have a script called matlab that is shadowing the original matlab command and so perhaps matlab is not receiving the -desktop flag which it needs to run when launched without a terminal.

See this entry for more details about getting the launcher to start properly by using -desktop.

If for some reason you still get nothing, try setting the type field to terminal application to diagnose the problem further.