Dell Studio 1555 Laptop SHUTS DOWN

Dell Studio 1555 Laptop (X640SHUTS DOWN. OS = Windows 7 Pro. This happens at random within a few minutes to several hours after boot. The problem started to occur about mid September, 2015.

Windows updates have been done.  In MSConfig, all drivers have been updated.  Heat does NOT appear to .be   a problem.  The shutdown is not common to any software or operation.  Upon rebooting, a Windows message appears indication that Windows has not been properly shut down.  I choose "Start Windows Normally" and the computer boots okay, then ultimately again shuts down - not sleep - but like the power was completely turned off.  The battery is fully charged and does not appear to be a factor.  This occurs whether or not the power cord is plugged into the computer.  I attempted Dell Diagnostics, it is not effective.  DD installs the System Detect but does not proceed beyond that point - even after several hours.  Eventually another complete shutdown happens. 

I have run deep scans (Norton Security Suite) without finding any malware or viruses. I have also run Norton Power Eraser without it detecting anything. NSS load upon boot and checks every site and email.

I would appreciate any input toward resolution of this shutdown problem.