thank you for the advice. It seems
it was the ignition switch.

I tried the ignition switch with a screwdriver
before putting it to place and the car started
and the lights turned on when at position "II".

To take the old one off was very tricky (don't know
people on the websites describe it in 3 steps!)
We had to disassemble it, otherwise there was no space to take it out.
Also, putting the ignition switch in place took very
long time, because we had to disassemble and assemble it again
to put it to place.

Now for the bad news and to make the long story short...
It seems that the first time we put it back, we didn't place
the clip on (which holds the prongs in place), so when we
put the wires on the switch probably some of the ignition switch
prongs were pushed back. When we turned the engine on again (using the
key now

), something shorted and burned (we heard a 'tsaf'). When I opened the
fuse box

it looks like the part on the bottom right where some cables come in
the fuse

box burned.

Next time that we tried to crank the engine, there is no crank
and I see some small indication of smoke from the negative pole
of the battery(!).

After that we placed the ignition switch properly, but the bad
was already done. So now, when turning key to ignite:

0. At "II" indicators will light
1. At "III" no crank
2. Smoke from neg. battery pole
3. Bottom right part of fuse box when some cables come in, seems
to be burned. (will post picture if necessary)
4. Battery is ok though (still at 12.5v)

Thanks for your previous advice. Any suggestions now?
Can that burned part be replaced? I think I have to cut some
cables and reconnect them. I hope I don't screw up more after that...

michael