Linksys Wireless Router :: E1200 - Password Protecting Network?

I have been trying for the better half of the morning and afternoon to configure my family's wireless network. In particular, I would like to password protect the Wifi in such a way that every time I disconnect from the internet, a password is required to reconnect.I have setup the password and confirmed that it works properly when other machines in the house try to connect; however, the main computer I have used to set everything up is also a shared computer. Every time I disconnect from the internet and reconnect, it automatically connects without requesting the Wifi password.
 
Because it is a shared computer, I would like to disable internet access while I am away but leave the rest of the computer functional. Creating separate user accounts is not an option at this time.Is there any way to require that every computer submit the Wifi password after disconnecting and attempting to reconnect?