Without more information, it's hard to know what is happening, assuming it's getting stuck on the license check
Has Maya ever run on the machine ?
Use Apple's Activity Monitor application to get a sample of the Maya process to see where it is
Are there any dialog windows underneath the Maya splash screen
Check the log files in /tmp/Adlm.log
From a terminal window run Maya directly to see what messages if any are output
export FLEXLM_DIAGNOSTICS=3
/Applications/Autodesk/maya2016/Maya.app/Contents/MacOS/Maya
Do you have any "extended" characters in your home path, in case the locale is causinfpg problems
Have you tried to reboot the machine, it's possible the mutex used for licensing gets locked and needs to be cleared
Wayne Arnold
Developer