1988 Buick Riviera will crank but won't start. It back fires then stalls and dies. Replaced the fuel pump last week and it ran good for the days then nothing...

Have you had the catalytic converter changed ever? Have you the owner manual? Are there any new lights in the dashboard? Some vehicle are computer programmed to stall after a certain number of miles to prevent further damage. That is what it sounds like is happening to you.

There is no thinking & throwing parts at any vehicle

The only fix is knowledge & the ability to do some testing

Lets go with a failed fuel pump & at least check pressure
at the motor on a gauge or see if that data is on a scan tool

Explain what test told you a cylinder wasn't firing !

Check the battery cables. I had the same issues with my 96 tacoma, The battery cable connection at the battery can be cranked down but still be loose. Hard to explain, doesn't make sense, but just check it out.

If it is a 3.8 engine change the crank sensor,they go bad on the 3.8 engines.

last year, OBD1 car (dumbb ECU)
no scan tools for it
if you run on the road with that hack , and wreck
expect a nice fire. fuel fire.
if you used a voltmeter and say 12vdc there, all hotwiring stuff
need not be done. (
it stalled (misfire)
and then would not what? start but cranks ok?
4wd?
3sp ,4sp auto or 5speed stick
16v engine or 8v, both are G16s but EFI radially different.
16v is MPI with 4 injectors, 8v is 1 injector TBI
try a new
cap,.rotor spark wires and spark plugs yet?
cant burn fuel with bad spark
i guess the cam bent did not slip as it run ok later, but is 60,000 mile belt. and will slip ignored.

next time it stalls
check headlamps they work, and all electric
then see if CEL glows key on, i must or ECU lost power
it has 3 fuse that can rust, IG coil, FI, and DOME.
the CEL must glow, is first checks.

unplug the cam sensor behind the water pump pulley; see if it starts; if it does, shut off engine; replace both cam and crank sensors because crank sensors go out in these engines

change electric coil ,fuel filter,

leak in the air hose would send to much oxygen to the engine and causing a stall

But is it getting fuel to the Carb? and have you checked to make sure you have fuel pressure? Also spark?

fuel filter,or pound on fuel tank lightly while trying to start with rubber mallet