without any output why it won't start it's a bit hard to help.
I extracted Singularity to /home/lockheed/downloads and I simply start it via Terminal (start Terminal first, it's in System Tools section) which should bring you to your home directory:
This means: username/loginname (lockheed, hostname (lovelock), current folder (~ is a shortcut for /home/username), prompt ($ means usually normal user, # would mean admin mode (called "root" - never work in root mode unless doing admin stuff)
then simply start the viewer by typing:
lockheed@lovelock:~$ downloads/Singularity_1.6.0_3/singularity [ press Enter]
of course, use your extract path and file name.
Then the Terminal should stay open and give a lot of text what is actually happening.
Hint: for lazy typing, there is an auto complete option when the path is clear, try using the TAB key when you type:
lockheed@lovelock:~$ Down[press TAB key and look what happens]
In case the path is not clear, press TAB twice to see possible options basing on what you typed so far. Also works with commands and file names.
The Terminal is your friend.