Hallo,

I start with "cold and dark" Option"

I Switch battery on and Attach ground power.
In The book written by Tim Rommen I should in following steps 
turn both Switches on the IRS-Panel to NAV
and have to enter the current Position via CDU.

But the right CPU is dark so I can not use it
and get a peep-tone unitil I turn the right Switch to OFF again.

Please for tips for reasons.

This sounds like a power issue.  If the CDU and both right and Lower DU aren't on this ground power did not connect right.  I'm by no means an expert on the 737.  But the tones might be something along the lines of IRS on Bat.  Look above the Right IRS selection knob.  Top right light is ON DC.  If that is illuminated power is definitely your issue.

2 hours ago, attila20 said:

Hallo,

I start with "cold and dark" Option"

I Switch battery on and Attach ground power.
In The book written by Tim Rommen I should in following steps 
turn both Switches on the IRS-Panel to NAV
and have to enter the current Position via CDU.

But the right CPU is dark so I can not use it
and get a peep-tone unitil I turn the right Switch to OFF again.

Please for tips for reasons.

You have connected the ground power, did you move the ground power switch to ON to give power to the aircraft?

Thank you Brian,

I did a silly-very-beginner-fault:

I thought, when "ground power available" is lit,
I have it,
but you have to kick the Switch down too.
That was it.