Q: input type=image - onclick(), will trigger its event , but not act well on function in jquery (I think this could be two posts - 2 questions.. so if you'll comment on it... I will separate those)
the main issue is acually:
how could I set an image-background for a button... easy & properly ?
I think that now I could be sure about these facts:
as I had a "little" problem with setting image as button-background ,
...I thought, ok, if it's difficult to set <input type='button'> with image-background, why not instead , just set onclick event on a <input type='image'>!
and I was right(...almost), cause yes, to set click-event on  image type is easy, also,  to set src ..instead of background-image for button... at least for me, it is. 
the problem is, in current project), using a jQuery-UI  dialog - ok, cancel,
seems that the problem is that image-type , Posts back (?!), so dialog disappears 
and button does not  cause this flaw.
I tried to debug it with a break-point, in vs2010 and it both ok with a click event as they both get to the point of "function entry" ... so with the image type ... i could only notes, as i could see the <- Back button, toggles from disabled to be clickable, so it means it did post back. 
and that does not happen with a button , as you hover over the button nothing happans , and with image you could see a link in status bar .
so there is a difference (a real one), between button-"convert" into image,  than an image turned into a "button" (attaching it with a Click() event) , 
so what i would like to know , is: (only if I am allowed this time to use this post for both answers as they realy relate) 
why does image post back? could i disable this action?
 ...it is not a server control. is that something you should know, and that suppose to happen ?
again if it is off-topic i would move this question, and i do need a propper way to set the background image for a button unless there's a workaround for it's behavior.

A: I'm not sure why the image type input element behaves differently than the button type, but if I were you I would avoid it all together. If you are looking to customize your button (which it appears you are) I would suggest using a div and control the user interaction via jquery/javascript. 
Demo: http://jsfiddle.net/jrb9249/BvTD5/
HTML:
<body>
    <div class="div_button">
        <p>Click Me!</p>
    </div>
</body>

Javascript:
$('.div_button').click(function(){
    alert('Run a postback via JS');
});

CSS:
.div_button
{
    border: solid 1px gray;
    width:80px;
    height:25px;
    background:#A3A3A3;
    text-align:center;
    margin:0 auto;
    margin-top:50px;
}

.div_button:hover
{
    border: solid 1px blue;
    background:#A1A1A1;
    cursor:pointer;
}

To add some finishing touches to complete the button look, just add some rounded corners using the jquery rounded corners plugin found here. And if you need to do a post back with this control (it doesn't look like an asp.net control so I don't think that is what you are doing) you can use the __Postback technique described here.
I hope this helps, good luck with your site.

Update:
Since this post I've started enclosing my div tags within an <a> tag to create a hyperlink out of the div. You can then apply custom click events to the <a> element and have greater control over the button you created.
