I installed new Sears gdo and the wireless clicker keypad I have that I bought from sears some time ago, I cannot re-program it is model number 139-18731 do you know which programming instructions are right for this model?

Go to this website for complete directions plus a video.

http://www.chamberlain-diy.com/doityourself/pages/productmodeldetail.aspx?modelId=1477

First, check the battery inside the keyless entry. It may have died and that is the whole problem. Replace it if necessary. If it has never been replaced previously, you might want to do that now anyway..
On the GDO there is a "smart" button located by where the wires are connected.
Press and release the smart button. Enter your code slowly and press enter. The light on the GDO should flash off and on to let you know the GDO has memorized the code.
Good Luck..

Locate the smart/learn button on the rear of the motor unit near where all those white wires go. Press and immediately release this and then walk over to the keypad and key in any 4 digit code you like and press enter.

Your problem is not your logic board. If when you program one remote it causes the other to not work then you have a bad remote. The only solution is to buy a new remote (same model number) and then by a process of elimination finding the culprit. You will find one of the remotes will not work with the new one but the others will.

If your opener doesn't have safety sensors in the doorway this keypad will not work with it.

No the clickers will only work with openers with sensors.

No.

Give Chamberlain Technical Support Hotline a call at 800-528-5880. They will help you.

It is really important to that you have the correct remotes for your opener. The model number is on the end closest to the door and starts with 139.

is it locked. does door lift manually. are springs/cables ok?