Welcome to the forum.
Is the engine flex fuel or gas? What engine? Possibilities are 4.8, 5.3 and 6.0. For the sake of moving on I am going to assume a 5.3L. All 03 Denali's do not have the same parts.
Agree with @PNWTahoe about a possible injector problem. How old are the ignition components? Pull the plugs and inspect. Post pics of them here. That is just to react to fuel pressure but that 35 psi is not enough.
Flex fuel: https://www.rockauto.com/en/moreinfo.php?pk=7056044&cc=1415551&pt=10147&jsn=893
Gas: https://www.rockauto.com/en/moreinfo.php?pk=1300750&cc=1415551&pt=10147&jsn=892
Fuel pressure regulator-flex fuel: https://www.rockauto.com/en/moreinfo.php?pk=344238&cc=1415551&pt=6124&jsn=904
Fuel pressure regulator-gas: https://www.rockauto.com/en/moreinfo.php?pk=1029862&cc=1415551&pt=6124&jsn=90
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