Lately whenever I click on the Recycle Bin or MyComputer a screen pops up asking to establish an internet connection. The screen stays for a few seconds or until I click on the shutdown icon. Any idea what is going wrong and how to fix it.

Very strange behaviour. It sounds like the internet connect has been associated with your other two folders. First thing is to do a virus scan, like now...... Second is to do a Scan Disk and see if it will correct. Third is to go to System file checker and see if you get errors there with option to correct and finally forth go to start, settings, control panel, internet, settings and see what is shows for connect to.