The Samsung Captivate is a USA-exclusive flagship Android phone in the Galaxy S class of devices, released by Samsung in March 2010 for use on the AT&T network. Identifiable by model number SGH-I897.
try taking the fascia off using the guides on the right and clean round the physical power button..you get a build up of sweat, skin cells and dirt that cause buttons to stick. This may be the problem here.