If you have a full splash screen, which it sounds like you do, I would use the transform trick.
The important thing here is that this solution does not need to know the size of your splash image- you don't need to change your CSS to accommodate a differently sized splash image.
The CSS is quite simple for this- basically you position the upper left corner absolutely at 50%, 50%; then transform the image by half of it's width and height to effectively move the center of the object to that window midpoint.
#splashlogo {
position: absolute;
left: 50%;
top: 50%;
transform: translateX(-50%) translateY(-50%);
}
/* Page styling, ignore this */
body {
background-color: #bada55; }
img {
box-shadow: 6px 6px 3px rgba(0,0,0,0.25); }
<div class="splashscreenlogo">
<div id="splashlogo">
<img src="http://www.placecage.com/300/300" alt="Splashscreen logo">
</div>
</div>