Engine not starting (G13BB)

This suggests that you might have the wrong cylinder head for that engine - I wonder what other differences there might be in addition to the camshaft.

Do you know what vehicle the refurbished cylinder head was originally removed from?

Also, do you know what market your car was built for - I think you said it was a 2004, by 2004 most Jimnys in Europe would have had the M13a engine, not the G13bb.

Is soft top version.
I don't know on which car was the cylinder head.. but I see no other differences, it fit perfectly, old camshaft also fit perfectly...
I would rule out damaged ECU because sometimes I see a isolated pulse on injectors 2 and 3. 
Now I replaced cpk sensor, I tested it on car, 450 ohm, ~300 mV when cranking the engine, ECU see if I disconnect it...

this is a G13.
most likely the wrong timing cam ring on the cam shaft or it is placed at the wrong timing.
there are different numbers of signaling tabs on the timing ring on different engines.
Can be moved over from your old head if it did not follow the old cam shaft over?
Pry it off the old and tap it back on the new cam shaft. Must be in the correct position but for some reason it is not so difficult to get it placed correctly, I done it a few times.

edit: usually only the later m16 has the crank sensor.

Edit2: It seems i have too little knowledge of the G13 engine in the spanish cab versions so little or nothing of the above applies to this problem..
 

It is the old, original camshaft installed 
It has no removable ring, just 2 lobes.

The camshaft for engine variant without crankshaft sensor looks different 
   
But I cannot use that in my engine with crankshaft sensor.
Timing is set, marks are aligned 

As you can see, I have both sensors, CKP and CMP 
This engine variant was used on European soft top Jimny. 

Was the cam position sensor in the replacement head the same as your old head?

I wonder if the diameter of the two timing wheels on the end of the camshaft are the same and sit in the same place?

If there is a difference in gap between cpk and timing ring between the two heads you might not be getting a good signal and this would cause the the issue with the injectors?

Yes, the same sensor. I replaced it too but no change.
So you're saying to compare the sensor case to be sure it fits in same position at same gap?
LE: is the old, original casing installed. New cylinder head came without it.