Wont start sometimes idles rough when first start, cut off

I have a 4cyl 1996 buick century. I have been having problems with it for over 6 months now. The car wont start som mornings, warm or cold, before i go to work. When i get home from work though it will fire right up! at first i thought it was the fuel pump because i didn't hear it *** on when i turned the key but i"ve replaced it. Since the car started having this problem It has also cut off on me while driving or Idleing in park. a few times i was driving down the road and the check engine light would flash on for a few seconds and my car would still run but no matter how hard I pressed the gas i wouldnot accelerated then the light would go away and i would have fuel pressure again. the light would go on and off maybe 3 or 4 times and then it would jus die. Another crazy thing that happend was another time it cut off while i was stopped at a red light and when it cut off, after sputtering, ( power was still on) the speedometer was jumping up and down from like 0 to 70 over and over again. the check engine light came on and off, the light was also getting dimmer then bright again. these has happened on quite a few ocassions. after it cuts off usually the lights stop flashing, i hear the fuel pump kick on and it starts right up. sometimes in just a couple minutes and sometimes a few hours. The check engine light always goes away after the car starts except once i to it to the shop and i believe it threw a 1600 code... a serial communication link malfunction. i believe i need to put a new computer in it but i want to be sure before i buy one. help please???