Hacked

I just went to work on a new theme and discovered that my site has been hacked. At the bottom of each page is a long list of garbage links. Here’s a little preview of what I’m looking at:

<!-- google --><font id="bxhbe"  color="e419b0"  style="height: 0;overflow: hidden;width: 0; position: absolute; font-family:courier; font-size:19px" >
xeex402109
<a href=http://hiretheitpros.com/analysis//a/d/corrigan91021.php>corrigan insurance md</a>
<a href=http://1times1.net/cursos/lrma/j/vanagon91021.php>rental vanagon oakland ca</a>

This is tacked on after my closing html tag. I’ve installed a new theme and viewed the site to see if that would resolve the issue, but the problem is still there. I’ve deleted all the plugins that I no longer need. Now I’m at a loss as to where to look, because it’s obvious that the problem isn’t with the template files and I’m not all that familiar with the rest.

So now I have some questions.
(1) If the problem is with a plugin, will deactivating the plugin deal with the issue, or do I need to delete it completely? I was thinking of deactivating all plugins one-by-one to see if I could find the culprit.
(2) Is there a way to re-install WordPress and still keep my database intact? I really don’t want to start from scratch. XD
(3) Is there a way to search all files for the code listed above, so that I can find the source of the problem directly? I’ve used the Exploit Scanner plugin, but there were too many false-positives for me to make any good use of the results.