Lots of good advice from dbltoe above which I won't repeat.
More specifically your header banner is a background image which doesn't affect the height of the table cell that contains it. The logo did affect this, but you have deleted, so the cell doesn't need as much space and has partially closed up. I'll talk about a solution to this in a moment.
The link left behind when your logo has gone is contained in a a file called includes/languages/english/header.php. You may already have a copy in includes/languages/english/YOUR_TEMPLATE_NAME/header.php file (YOUR_TEMPLATE_NAME is currently classic but see below). If not you should create one. You can then edit the following line in the new file> define('HEADER_ALT_TEXT', 'Powered by Zen Cart :: The Art of E-Commerce');And the animations? I'm afraid I'm not sure to which images you are referring.
OK, you have two possible solutions. Either faff about trying to get the table cell to match the height of your image. Or, take a step backwards and design as the Zen Cart development team intended you to do harnessing the power of the template_default.
As a new user you have defaulted to the classic template. This is intended primarily for backward compatibility with earlier versions of Zen Cart. I recommend replacing it with the Future Zen template which engages template_default and is the way forward, as well as being much easier for new users to work with. You can download it from the downloads section of this site, or by clicking on the link in my signature below.
At this point I would normally go on to tell you that you then need only change the values highlighted below in your stylesheet to make your header banner display properly. But in your case you don't even need to do that, since they are already set to the exact dimensions of your image> #logoWrapper {
width:760px;
height:110px;
background-image:url(../images/header_bg.jpg);
background-repeat:no-repeat;
}