Hardware or software problem, that is the question.
First, you can try to start the system in Safe Mode (press F8 during startup). If it works, it would make it more likely a software problem, which can be remedied by reinstalling the system (or restoring it to the factory state if that's an option) after you saved your important files to an external drive.
Second, you can test the memory by running Memtest ( http://www.memtest.org/#downiso ). Of course you'll need another computer to prepare a bootable CD or USB drive.