Hey..
First of all some movies, will make things clearer..
When I turn the key to ignition sometimes its like that:

http://pl.youtube.com/watch?v=W65V2Tw2hOw

and sometimes its like that:

http://pl.youtube.com/watch?v=6mA8BH3NQJI

And I cannot find any particular reason that makes tha change..

The car cranks, but there is no fuel pump.
I had before 2 or 3 times the situation that while driving SES showed up, and then the rpm drops, but it was for a second so it all came back after that.. Then I changed alternator which died and all went back to normal..
And after a half of year or something I had this kind of situation again
(I had to even push gas pedal a bit while standing on traffic lights - manual transission - so It would not die..).. But theye were all for 1/2 secs and all went back to normal.. And once the SES light blinks like that on the movie at the ignition, but still I was able to start the car and all was fine for a couple of weeks.. And now the car died..

Any ideas? Btw. its Firebird V6 '88.