The computer is the least likely cause (unless the vehicle has been in deep
water before this began; the ECU is on the floorboard.) My first thought is
the "main relay" - the fuel pump relay - which has a very long history of
symptoms like that. See TeGGeR's FAQs at
http://tegger.com/hondafaq/faq.html#startrun for the details and other
ideas.

Mike