Also, be sure to let us know if you're exporting to a second to external drive -- and, if so, if that drive is formatted NTFS or FAT32 (which has a file size limitation).
What type of camcorder is your original video coming from and how did you get it onto your computer?
When you set up your Premiere Elements project, which project settings did you select?
Also, if your project aborted 85% of the way through, how do you know the file you were outputting was 1.6 gig in size?
In the link that Neale provided, be sure to see the BSOD - A Serious Issue link.
When your computer reboots on its own, you have suffered a BSOD (Blue Screen of Death) occurance, whether you see the blue screen, or not. What happens will depend on how you have your OS set, when it encounters a major error.
The main causes of a BSOD are hardware related, with a problem driver interferring with the OS the second most common.
This IS a serious issue, and should be the very first thing that I researched.