This really sounds like a virus or other malicious coding.
Restart your computer, login as usual, then bring up a command prompt (start >> run >> type in "cmd" without quotes) and run it >> type in "shutdown -a" without quotes and press enter. See if it says that it aborted a shutdown - if so, very good!
Now go to your web browser and go to http://www.filehippo.com/
now look in the middle section and find AVG Antivirus 7.5... Download it, install it, update it, do a full system scan.
Come back with any problems that you encountered (and the results of the scan).