It only happens with a cold boot but it doesn't happen all the time.
Sometimes it will work fine when I first turn it on.  Other times I
have to hit the reset button 2 or 3 times before I can get a game to
start.  If I press CTRL+ALT+DEL it will show "This program is not
responding." next to the game in question.   Dxdiag.exe shows no
problems.  The problem may or may not have anything to do with
DirectX.  I do know that the problem only occurs when I try to open an
advanced type game that uses DirectX.  As far as the simple games like
Solitaire and Free Cell that come with Windows I've never had a
problem with those.  The problem is mostly a nuisance.  The first
thing I try to do when the computer finishes booting up is to try to
start a game program.  If that program loads okay then I know all
other programs will load as well.  Since the computer isn't connected
to the internet, there's no antivirus, or spyware protection, or
firewall protection on it.  It's just Windows XP Service Pack 1 and
whatever programs I put on it.  I'm using DirectX 9c now but the
problem occured with earlier versions of DirectX too.