I am a little confused. You say it is flashing, but then you can't click on icons? If it was the display itself you should still be able to click on things. However if it is software, then clicking could be a problem.
When you say you reinstalled the system using recovery, I am assuming you mean you used the "System Restore" to revert back to an old point? If that is the case, the problem may not have been removed.
Also the fact that it happens in "Safe Mode" makes it even less likely to be a software issue, unless it is the Windows system itself.
However, if you were able to use the "System Restore" you would have had to click on something. Please clarify the information so that we can better understand and assist.