Q: No internet connection and programs aren't staying open

Restart your modem/router and test again.

How are you trying to connect - Ethernet, Wi-Fi....?

Permission Issues - Troubleshooting

You may need to rebuild permissions on your user account. To do this,boot to your Recovery partition (holding down the Command and R keys while booting) and open Terminal from the Utilities menu. In Terminal, type:  ‘resetpassword’ (without the ’s), hit return, and select the admin user. You are not going to reset your password. Click on the icon for your Macs hard drive at the top. From the drop down below it select the user account which is having issues. At the bottom of the window, you'll see an area labeled Restore Home Directory Permissions and ACLs. Click the reset button there. The process takes a few minutes. When complete, restart.   

Repair User Permissions