Intel iMac Issues

Question

Just purchased the new 2.66 Intel iMac with the 20 in screen with 4 gb RAM and running OSX 10.5.3.  In the past week the Mac has started to shutdown unexpectedly (with all power setting turned off) and reboots itself.  Also, when first booting up, the Mac will chime and get to the gray Apple screen and restart.  This will continue until it loads the desktop and then restarts again.  This will go through a cycle of 3 to 4 time until it finally settles down and let's me get to work!