1999 Pontiac Grand Am Fuel pump and fuel sending unit? Diff

I have a 99 grand am that failed to run. It would turn over once and run for like.875 sec. (Estimate) Then shut back off after this it would only turn. It will do this every couple of hours if you leave it and come back to it.

I thought it was the fuel pump as the fuel gauge had been giving false readings for months. I found a used fuel pump at a salvage yard and replaced it but had to use the old float (sending unit?) As it did not have one.

Could the sending unit (Float assembly?) Keep the car from running or causing these syptoms.