Engine is not running

So I got this car listed above I have a problem that I think might be fuel related. Previous owner had car just parked catching dust but car started quick with a new battery so I just needed to get rid of check engine light and address some P0171 code and a P0174 for emissions to pass the car. So car was running and one day wouldn't crank at all. So when someone told me to disconnect the battery and reset the car and then try to turn it on. So I did and car started right up but would run for a bit and just shut off completely, so I turned ignition and checked my fuel pump without starting car and checked my relays but I don't know if they work or not so I figured it was the fuel filter because I purchased spray for the carburetor and tried to keep car running like that, but it would still shut off. Now that I changed the filter the car just starts but won't crank over at all now I tried to reset the inertia switch but I'm not sure if it works or not? How can I figured that out? And any advise on my problem. TIA