Windows 7: Computer shut down during memory test.

I have been having problems for a few days now. Would not start up. (press power button, fans start, no beep, no image on monitor.) This happened many times and still is, at one point it crashed and had bsod, also a white screen at one point...



I checked the hard drive with a diagnostic tool, said it was all fine, I then began to suspect the ram.
A few mins ago I started a memory test using the windows 7 memory diagnostic, it started fine after it restarted the computer, when it got to 20% overall however the computer shut down completely and would not turn on, this time no fans started, no beep, nothing at all.
I turned it off on the mains and waited for a few mins and tried again, it worked.

Now I am totally clueless, I don't know if the memtest crash was because there is a fault with the ram or if something else caused it. Any help would be appreciated

Please follow the Blue Screen of Death (BSOD) Posting Instructions

Is that still relevant if I don't get the bsod? (Only had it once and not since)
Also the diagnostic tool doesn't seem to work...

************** Exception Text **************
System.IO.IOException: Could not complete operation on some files and directories. See the Data property of the exception for more details.
at Microsoft.VisualBasic.FileIO.FileSystem.FxCopyOrMoveDirectory(CopyOrMove operation, String sourceDirectoryPath, String targetDirectoryPath, Boolean overwrite)
at Microsoft.VisualBasic.FileIO.FileSystem.CopyOrMoveDirectory(CopyOrMove operation, String sourceDirectoryName, String destinationDirectoryName, Boolean overwrite, UIOptionInternal showUI, UICancelOption onUserCancel)
at Microsoft.VisualBasic.MyServices.FileSystemProxy.CopyDirectory(String sourceDirectoryName, String destinationDirectoryName, Boolean overwrite)
at SF_Diagnostic_Tool.Form1.Button1_Click(Object sender, EventArgs e)
at System.Windows.Forms.Control.OnClick(EventArgs e)
at System.Windows.Forms.Button.OnClick(EventArgs e)
at System.Windows.Forms.Button.OnMouseUp(MouseEventArgs mevent)
at System.Windows.Forms.Control.WmMouseUp(Message& m, MouseButtons button, Int32 clicks)
at System.Windows.Forms.Control.WndProc(Message& m)
at System.Windows.Forms.ButtonBase.WndProc(Message& m)
at System.Windows.Forms.Button.WndProc(Message& m)
at System.Windows.Forms.Control.ControlNativeWindow.OnMessage(Message& m)
at System.Windows.Forms.Control.ControlNativeWindow.WndProc(Message& m)
at System.Windows.Forms.NativeWindow.Callback(IntPtr hWnd, Int32 msg, IntP