No pressure runs fine but no pressure

Could be a fuel pressure regulator not working. Thus ecu complaining about fuel Pressure. probably not enough because the regulator is worn and leaking down so will not maintain the proper pressure. You will need to google the make model and fuel pressure regulator to find it's location or library and repair manual. Otherwise, you need to measure the pressure and find the spec for the required fuel pressure. Probably somewhere around 120PSI

Sounds like a faulty fuel pressure regulator, or possibly the MAF sensor.

Most people recommend replacing the motor capacitor in this situation, since a faulty cap will reduce the starting torque. But in my case the check valve was the culprit - there was too much back pressure on the head.

start capacitor is NOT ok. Check the centrifugal switch in the motor to see of it's not stuck in the run position too.

You could change the oil pressure sending unit to see if it is faulty, or have the oil pressure checked with a mechanical gauge.

sounds like you have a stuck pressure release valve inside the pump

Please Check High pressure fuel pump. In my opinion your fuel pump connected to timing belt is giving away. When you increase rev on engine, the pressure increases as well. As a result, Injector spray pattern gets steady. But on revs below 900rpm it struggle to maintains required pressure. If everything in fuel injection system is working fine then the Worst case scenario is that the head pressure is leaking aka compression leakage.

If it acts like it is flooding while idling, but it runs fine on the road, it could be running too rich and flooding it out due to leaking injectors, bad fuel pressure regulator, or excessive fuel pressure.

I would start by replacing the Fuel Pressure Regulator since it doesn't cost as much as the injectors.
Check your fuel pressure using a Fuel Pressure Check Gauge to see if the fuel pressure regulator is maintaining the proper pressure.

Vacuum is attached to the Fuel Pressure Regulator to control system pressure. When the fuel pressure regulator is not functioning properly it causes the fuel pressure to be above normal operating pressure. This condition causes excess fuel to be injected causing a rich mixture that produces black smoke.

I’m happy to help further over the phone at https://www.6ya.com/expert/jeremy_69f3cc28d95bf514

If you remove the tip, will it work? If so, unloader valve is sticking and needs to be removed and lubed with lithium grease.

you have a unloader or bypass valve on the machine & it sounds like that is sticking.
take out and lubricate