David, assuming the X51 has a similar OS schema as the X51v, you can go to Start-->Settings-->System tab--> Power-->Power Button tab (may need to scroll to the right on the tabs to see
it), then select Full Power Off. Now holding down the Power button
for a couple of seconds should give you a prompt to actually power
off the device instead of merely dimming/turning off the display.
Studio XPS 16 / Intel Core 2 Duo P8600/ 4GB DDR3 / 512MB ATI Radeon HD 3670 / 64-bit Vista & Ubuntu