Your problem appears from your description to be a misbehaving network-manager. To find out more information about the problem it's important to gather up the output from network manager as it's attempting to make a connection to your wifi network.
Before you follow these instructions, please save these instructions, what we are about to do with disable your internet on the machine and you may loose the ability to read how to switch it back on if you don't save them.
The instructions to gather the information will need you to go into a command line, you can simply go to the search button in the left top corner and type in 'command', you'll see a little black screen icon called 'Terminal' click on it.
Firstly we must stop the network manager by copying and pasting this command. This will ask you for your password:
gksu service network-manager stop
Next we want to start the manager and capture the information from it:
gksu NetworkManager --no-daemon &> ~/Desktop/debug.txt
It shouldn't return you back to the prompt. Now with this running attempt to connect to your wifi service through the normal means. You should have noticed the network icon in the right corner disappear when you stopped the service and reappear when you started it again. Try a couple of times to record a few instances in the log file.
You'll notice a new file on your desktop called debug.txt, you need to send this to who-ever will be debugging your problem. In this case you should attach it to this question by editing the original question (don't post a new answer) add in the log file contents.
To start the network-manage properly you should hold [ctrl] and press [C] this should stop the special network manager service and return you to the prompt. Then simply type this command to start the normal service again:
gksu service network-manager start
We'll work out what your problem is from there.