95 honda only starts after 30 second key on wait...help

My 95 Honda accord 4 cy. vtech, will turn over but not will start, you can try unlimited times and it just cranks, but no fire or start.... UNLESS I wait about 30 seconds first.  In this time what happens is, for 15 seconds the usual dash lights are on, including check engine light, at 16 seconds the D4 green transmission light starts to flash rapidly.  At 30 seconds the main relay can be heard to finally click in, and the fuel pump whirs and primes the fuel system for 1.5 seconds and immediately the check engine light turns off, the D4 light turns off,  and the fuel pump also stops whirring.  AT this point, at any time from here on out, (until you turn the car off again) you can turn the key the rest of the way to start, and the engine cranks over and now immediately starts right up!
Sometimes all the above happens just as described, but the D4 transmission position light does not start to flash.  Everything else happens the same way and timing and after 30 seconds the car will start.  NOTES:   a. The obd trouble codes do not flash any codes when the jumper is put in place to read the codes.   b. I have removed and checked the main relay, looked ok, and just in case I re-soldered all connections on the main relay board.   c.the car drives and shifts fine.  d. The time frames are exactly the same every time.  Electronically perfectly the same, like the computer finally decides, OK go ahead and work now. Or like the car is attempting by some programmed response to say that something is wrong and needs attention.  
Thank you...I hope someone knows what causes this, please advise.