Without the compressor running, the system must have around 60 PSI to run. However, I suspect your system is filled with mostly air. You must vacuum it out and reinject it with R134a.
Sure, you can have system runing at 35 PSI but very little refrigerant in the system.
Autozone loans out vacuum pump for free. See what the sticker in the hood area say how many oz. your system takes.