Press the Windows key and "R" at the same time to open up the "Run" dialog and type in "msconfig" (without the quotes) and press "Okay".
This screen should appear:
Select the options as shown above (Pick "Selective startup" and uncheck "Load startup items") and hit "Apply" and then "Okay". Now, reboot your computer, ignore the message that comes up (it will tell you you're in Selective startup), and run the Blizzard SystemCheck application again as administrator.
This will hopefully fix your problem (a background startup program is likely interfering with the SystemCheck application). Afterwards, go back into msconfig and change it back to "Normal startup".