I have a 2001 Chevy tahoe won't start It sounded like it was still running when turned off I bought a new battery also a new fuel pump the truck is able to without the key
You would here the fuel pump prime up for a few seconds with just the key in the on position. You may have other fuel issues, I would do a fuel pressure bleed down test, this would tell you if the regulator, spider lines, or injectors are leaking. Fuel pressure should be 56 to 63 lbs. Have a fuel pressure gauge hooked at the Schrader valve on top of the intake, let it build up pressure with the key on, then turn the key off and watch the pressure. It should not drop more than 5 lbs. and hold that pressure for 3 minutes.
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