Moving this thread to the Installing Flash Player forums.
Could you please let us know the Windows version you use?
The computer is a Dell Latitude D620 running Windows XP SP3. Its got 2 GB of RAM, so that should be enough to install and run Adobe Flash Player.
I tried installing Adobe Flash Player 11 and when that failed I tried Flash Player 10, which also failed with the same error above.
That is an error I have never seen before.
What is the file version of KERNEL32.dll in C:\Windows\system32 ?
Can you post the contents of the FlashInstall.log file in C:\Windows\system32\Macromed\Flash