1991 Buick Lasabre

Hello, My wife has a 91 Buick Lasabre. After she drive's it about 20 block's or so it will start to sputter as if not getting enough gas then it will die. She restart's it then it run's very rough and goes maybe a block or so, then die's again. Next it will let you restart it but it will die imediatly when you touch the gas, either lightly touching the pedal or trying to "gun" it. After we let it set for about 8 hour's or so it will let you drive it about the 20 block's or so and the problem persist's. We replaced the fuel filter and it did'nt change anything. In the last year we have replaced the fuel pump for what I thouht was an unrelated problem. We took it to a part's store and it did'nt show any problem code's. It's over a 100 thousand mile's. Any help will be appreciated. Great web site by the way! Thank you.