Without special software and reinstalling Windows I suggest:

1) If IE is inaccessible, on another PC: Download an anti-malware application such as Malwarebytes onto a flash drive. If IE is accessible, download the application to your local drive
2) Boot your problem PC in Safe Mode with Networking, login with an admin account and update your AVG definitions then run a full system scan
3) At the command prompt (start menu > run > type in cmd and hit ok) type in:
REG ADD HKLM\SYSTEM\CurrentControlSet\Control\SafeBoot\Minimal\MSIServer /VE /T REG_SZ /F /D %Service%
4) Now type in: net start msiserver
5) Install your anti-malware application you downloaded to flash drive from step 1. If you dont see the flash drive, check Disk Management and assign it a drive letter
6) Run a full scan with your anti-malware app
7) Although the AV and anti-malware apps will find the suspicious files, I always doublecheck the work it did. Go to c:\windows\system32 in detailed view and sort by date. If you find any .dll's or .exe's with suspicious file names that have been modified within a few days, rename them with an appended .bak extension.
8) Since you've noted that you cant shutdown or restart, lets open the local group policy (start menu > run > type in: gpedit.msc) and navigate to: 'Computer Configuration\Windows Settings\Security Settings\Local Policies\User Rights Assignment' and find 'Shut down the system'. Add the Administrators group.
9) Reboot into normal mode and test the stability and determine if more needs to be done to correct the problems the malicious software caused.

Steps 3 and 4 are required to run the Windows Installer service which is needed to install your anti-malware app. If you run into any roadblocks just let us know.
Thanks,
Travis