No I’m so stuck right now. I cannot turn the wheel whatsoever when the vehicle is at a dead stop. When I jacket up in the air, I have no issues whatsoever of course but It also seems when I turn it on and off while in the air the power steering seems to help a little bit.
You need to pick up a power steering analyzer, they come in the HMMWV tool kits, 57K0267 and 57K0268 and test the pressure/flow of your steering pump.
You should at least have the kit 57K0267 to properly maintain your HMMWV in the the first place, I see one on fleabay for $400 shipped, if you look around you may find one cheaper, that kit has a ton of useful tools that will help you maintain your truck, the 57K0268 kit is more comprehensive and even includes a motor lift device which most folks will never need.
Just because you have a "new" pump does not mean it is working correctly.
I have also seen the PS analyzer kit sold separately for under $100 but suspect they may not be complete..