>>>But I found solution to my problem (from a message on Stackoverflow). What I needed to do is following: Enable all button at design time. Then disable those that need to be disabled in jQuery (in script). This way the post back (or no post back) that I set up at design time work.
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>>Glad you got it working - but it occurs to me that if neither button should ever initiate a postback then it would be better to use a simple HTML input control rather that asp:Button in the markup so that the problem doesn't arise. i.e:

<input type="button" id="button1" value="One" />

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>Very good point. I kind of forgot that you can use plain HTML input instead of aps:button. The only thing I am thinking right now is in this case I have 4 buttons (centered on the page). And 3 of them don't need to post back but one does. I want to be sure that they all have the same "look and feel.". Will having one as asp:button and others as html buttons affect it?

Depends on what you have in the css. If it's the same for input type='submit' and type='button' (which I see it is in the template Site.css) then they should be the same....