Ok, so we arent looking at any obvious spyware, but that doesnt completly rule out a malicious element to this problem.
When windows shuts down, it has a huge amount of work to do, to safely ensure that when you start her up again, everything runs smoothly again.
Have you tried looking at the task manager to see what programs are running just before you turn the pc off ??? press Cntrl >Alt > delete at the same time , to open up the task manager.
Once in the task manager,, click on proccesses and see whats running. Is there anything that you recognise that you thought wasnt running ???
Also,,, when was the last time you deleted cookies, history and internet files ???
Cookies ect can take up a lot of time,, but usually slow a pc down when its running,,, but its worth a try.
Remember,,, if you delete history, tempory internet files and cookies, you will loose stored information such as passwords for forums etc.
Go to my computer > change a setting > internet options > then click the boxes to delete old files and cookies.
I do this regulary on my pc,, it takes a few seconds.
Cookies and temory internet files dont half take up a lot of space, and fill up quite quickly.
Get back to us after we have tried the above.
We have to approach these types of problems on proccess of elimination train of thought.