Here are some specs on his computer from his second post
here is a list of equip.i forgot to include :
ms windows XL pro
AMD sempron 3000+
ram 250gb
motherboard ASUSTeK K8N
hard drive 977gb

A K8N board and a Sempron 3000 CPU, that would make it 5 years old perhaps, have you ever removed the side and cleaned out the dust bunnies?
What security programs are you running and when was each last used to scan the computer?
You show 250 gigs of RAM, I presume you mean megabytes. If so that is a small amount.

There is no mention of a video card, is it built into the motherboard? The full 6 digit designation for the mobo would help as there are numerous versions of that board.

Did you build the computer yourself or have someone do it for you?

250 giga bytes , computer status protected by windows
total physical.......250 gb
available physical..1.71 gb
total virtual.......4.34 gb
available virtual ..3.59 gb
the video card is built in to the mother board
K8N (socket 754 ), NVIDIA ,nFORCE3 ,
yes i built it myself with help from a neighbor , i lost my right arm and leg and there are different cards i couldn't handle with one hand , i probably could have but i didn't want to break any , i am a hundred miles from a computer parts store .

Asus build a good board mostly, used many of them myself. Currently have a flaky Gigabyte board I need to replace with a lesser Biostar I have here.

computer status protected by windows
Are you suggesting you have no anti virus or no anti malware programs installed?

When did you last remove the left side panel and clean out the dust bunnies that tend to build up in these things? Perhaps the computer is shutting down due to excessive heat, try removing the left side panel for a while and see if that helps. This is not a permanent fix but will give us somewhere to start from.

If you feel it may be heat related you might try installing the free version of Speccy. This will give you lots of information including temp readings. You can also get these of course by entering the BIOS on startup but you get details without the computer being under load.

Is it only YouTube? If you try to play a video from another site, say Hulu, does the same problem occur?

Also, the computer is probably blue screening it's a fatal error and windows reboots when that happens. The blue screen is going by so fast you don't see it, Disabling auto restart on system failure is something you could try. This will display the blue screen STOP ERROR so you can read the Stop error. I have seen UTube cause Blue Screens or reboots. One of the solutions is to try and disable hardware acceleration. Here are the instructions for Windows XP to do that.

1 Choose Start > Control Panel.
2 Double-click Display.
3 Click the Settings tab.
4 Click Advanced.
5 Click the Troubleshoot tab.
6 Move the Hardware Acceleration slider to None.
7 Click Apply and then click OK to accept the new setting and close the dialog box
8 Click OK to close the Display Properties dialog box.
Restart Windows.

i have speccy and the temperatures run 33c to 49c .i have plexiglass panel on the side of my computer and i keep dust cleaned out as soon as i see it .
i have mcafee and windows anti virus .

Think first thing I might try is using something like RevoUninstaller on the most aggressive setting to uninstall the Adobe Flash players.. use the adobe flash uninstall tool after... then restart computer before reinstalling current flash players.

Here is a link that might be useful: 32 bit windows flash uninstaller/cleaner

i just clicked on a video link with canada.com and and i got a blue screen but not long enough to read anything and then it went black .