Mac Mini freezes / hangs

Brand new (<2 wk) old Mac Mini will work for 1-4 hours and then hang / freeze with the "beach ball of death". This appears to be a recurrent problem with Mac Mini's over the last 6 months based on other's posts.

Core i7 Duo processor will allow access to alternate desktop or widgets but unable to navigate / select anything. Presently debugging with Activity Monitor. Over half of 750Gb drive available so disk storage not a problem, no memory paging to speak of, about 4 of 8 Gb RAM free.

Upgraded from a trouble-free Mac Mini of 3 years and I've got this mess - HELP!