Hitachi twin stack problem.

You stated that the compressor started up fine. I'll assume it reached it's max psi then cut out. Then upon reaching it's cut-in psi the motor ran slowly for a few seconds, then kicked off. I also assume you mean check valve when you refer to the non return valve.
If this sounds about right then. The first thing I would do is bleed out all the air from both the tank and the pump supply line leading from the pump head to the tank's check valve. You can do this by simply loosening the fitting that attaches the line at the head or the check valve. Once done try running the compressor again.
The purpose of this is to check the unloader valve. This valve bleeds off the pressure that remains in the compression cylinder and the supply line up to the check valve. When functioning normaly it will bleed off this pressure once the motor shuts off. If it is not working correctly then when your compressor starts back up (once it is already been filled) the piston will be working against a psi close to the max psi.

If the problem reoccurs only after the compressor has reached it's max psi, then the unloader valve is most likely the problem. If however it will not start up at all even after a complete bleed then it has to be something internal to the pump and\or motor.

Please try this and let me know (or repost) your findings.
If it's the unloader valve I should be able to explain how to repair this valve.
Good luck.