Then installed avast notebook does not turn off.

Once installed avast does not turn off my laptop, the screen is closing, and will not turn off, I turn off the button, it will damage my HD.

What is the message on the screen when you try to shutdown?
Which was your old antivirus before avast?

What operating System are you using and which version of avast! did you install ???

Post closing of windows 7, when to turn off this.
I’ve done system scan found no virus
computer will not turn off

Avast Internet Secutity 7.0.1474

DELL Vostro 3500
Windows 7 home premium
Processador: Intel i5 2.40Ghz
Memória: 4 GB
Tipo de sistema: 32 Bits

dell machines often come with McAfee antivirus installed…or Norton on older machines

did your machine have one of those?
did you uninstall it before installing avast?

You might also want to give the following a try:
http://fixitcenter.support.microsoft.com/Portal?lc=1033

Uninstall norton, but still with the same error

the computer shuts down as far as the blue screen with ‘logging off’ in the centre of the screen but it will not complete the shut down which means I am having to hold power button to turn off

How did you uninstall Norton ???

Control panel

run Norton removal tool 26a. and reboot

http://singularlabs.com/uninstallers/security-software/

That only removed a small part of the program. You need to run the removal tool to get rid of the rest.
You can find the removal tool by following the link in my signature.