Well, to wipe that slate clean and try to fix this problem we will go through a list of instructions.
1. First off, go to
https://www.superantispyware.com
A.Download Free Home User Edition
B.Open Up Program Once Downloaded
C.Click on
Scan Your Computer
D.Now On This Page Make Sure the full system scan is checked off

E.Remove all threats once scan is finished. Scan may take a couple of hours so be patient.
F.Reboot(if prompted)
*note* This will get rid of any spyware that might currently be on your computer slowing down internet performance.
2. After this scan, we are going to get rid of all those unnessecary temporary files stored on your computer from the internet.
Go to Start>Programs>Accessories>System Tools>Disk Cleanup
It will now scan for unnecessary files

Once finished check off these boxes
Only
Temporary Internet Files
Offline Pages
Temporary Files
3.Click "Ok" *It will now delete those files*

4. Download latest Flash plugin. Yours may not be up to date.
http://www.adobe.com/products/flashplayer/
5.Now open up Internet Explorer
6.Go to tools>Internet Options>Delete Browsing History>Delete All *Just another delete of any temporary files that were left behind.*
Play a youtube video now. If problem still persists, post a reply.