I am working on this for several days. Here is the summary of what has been done and what is going on
My furnace is Carrier 58WAV or 58ZAV (it is downflow)
I do not get any voltage on my igniter (that's how things started)
I installed new igniter
By blower is blowing
My inducer motor is working fine, I get 115VAC
I do not get 24VAC on my pressure switch, but I know that negative pressure created continuity (Removed it and checked by Ohmmeter while creating suction on the tube).
I installed new controller board
I get error code 31
My two flame limit switches are working (I get 24VAC each contact-ground). Also I removed one, heated it up and saw it tipped.
Draft safeguard switch is not reading 24VAC but had continuity with or without power, I short it with wire-still no voltage to pressure switch, Is this switch suppose to react on heat or gas? I checked it for heat sensibility on my electrical range and unfortunately destroyed it (melted plastic part), so if it was for heat it was not working. I am going today to get new one and install but I have exhausted all my options. Do you think this may solve the problem? Am I on right track?
Thank you very much.

You now have 3 posts, please keep to just 1 post it is very hard to keep track of what you are doing. No you are not on the right track. It is not the pressure switch if you are not getting power to it.

You are right. I will keep only this one.
Today I bought and installed draft safeguard switch. No change.
While inducer motor is spinning:
Voltage on safeguard switch measures 1.5 Volts
Voltage on pressure switch measures 2.5 Volts
Voltage on igniter measures 3 Volts
Voltage on two limit switches measures 26 Volts each
Error code is still 31
Now I have new board, new igniter, new safeguard switch and no idea what to do next.
Can you advice. Thank you.

You need to find out where you are losing the 26 volts at, if the limit switch has power then follow the red wires to where they go next and find where the 24 volts have stopped. Post a pic of the inside of your furnace and maybe I can help more.

There is a rectangular plate (3"x2") on the back wall of the furnace where red wires are connected. After going through limit switches the go up and connect directly into flat white plug (along with other colored wires) which is plugged in into the board edge. Contacts on the rectangular plate read 26 volts.
I was trying to embed images but only got option to enter image URL (I do not know how to do that, I do not have my pictures on the web)

The only things that keep the 24 volt from going to the pressure switch are these.
Google Image Result for http://www.hvacpartsoutlet.com/ProductImages/RSLB1370902.JPG

Google Image Result for http://www.hogslat.biz/images/products/products/heating/pura-fire/G20-5046.jpg


There could be as many as 4 or 5 of them in one unit. Some are near the burners, and there may even be a small one on top the burner, or in the blower compartment.

Yesterday I found the problem and hope this post will help others. I had a lots of dust/dirt accumulated in the white connector going into the control board edge. After cleaning I got 25Volts on pressure sensor (not on draft safeguard switch though - any comments?) and my igniter start glowing and everything start working. I also found one defective limit switch attached to the blower (going to purchase and install).
Thanks for your help. It is appreciated.