Driving bipolar stepper motor

I am unable to get floppy's drive stepper motor running with Arduino. It runs just fine with motor shield (in current case the one from ladyada's shop)
The motor is bipolar 4 wires, 200 steps.
If I connect it directly to Arduino pins and execute sample code from Learning section in Arduino web page, I can only hear ticks coming out from this stepper motor and thats all.
I've successfully run 5 wires unipolar stepper motor with Arduino Stepper library, but in this case - absolutely no movement.
So maybe anyone have any idea what could be wrong?

Steppers I'm trying to run is just like these: http://farm3.static.flickr.com/2734/4024555377_54723dd74e.jpg

Are you trying to have the Arduino provide all the current to drive this stepper motor?

The Arduino is not going to be able to, and you risk damage to the Arduino trying.

I've successfully run 5 wires unipolar stepper motor with Arduino Stepper library,

You can't use the same code to run 5 wire unipolar motors and 4 wire bipolar motors. the sequence is totally different:-

See:-
http://www.thebox.myzen.co.uk/Workshop/Motors_3.html
and

Motors 4

Yes, i’m trying to have the Arduino provide all the current to drive this stepper motor, because I have no clue how to connect external power source (as there is only 4 pins and all of them are for running motor).

Yes, i'm trying to have the Arduino provide all the current to drive this stepper motor,

Then it won't work and you will damage the arduino's output pins. You need a current driver like a motor shield or those circuits I posted the links for above.