Firstly you don't need to worry about IE 7 and lower. Those browsers are old and if anyone still used them then shame on them.
Most websites including youtube post notices if you using an old browser and suggest upgrading.
Now the alignment problem.
I would start over with the site. It seems to me you don't know how to correctly float your element.
You cant float half the site left and half of it right. You should rather float everything in 1 direction and use width and margins to get the corrected positons.
Example of this is having main content on the left and a sidebar. You should float them both left then use a margin on the main content to give the needed spacing.
Also try removing all those social divs and replacing with ul and li.
<ul id="socials">
<li><a href="
thepetpapers.blogspot.com/"><img src="Graphics/Blogger-64.jpg" width="64" height="64" alt="blogger" /></a></li>
<li><a href="
www.facebook.com/pages/Paws-For-Thought/180432735349729"><img src="Graphics/FaceBook-64.jpg" width="64" height="64" alt="facebook" /></a></li>
<li><a href="
twitter.com/#!/thepetpapers"><img src="Graphics/Twitter-64.jpg" width="64" height="64" alt="twitter" /></a></li>
<li><a href="
www.youtube.com/thepetpapers"><img src="Graphics/Youtube-64.jpg" width="64" height="64" alt="youtube" /></a></li>
</ul>
#socials {
margin 0;
padding: 0;
}
#socials li {
display: inline-block;
list-style: none;
}
But even this does not solve the problem as your elements are floating around. You need to define each element and build a structure.
The "blue link boxes" are from not defining the css. Add a { border: none; } to your css and that should help.