I mean the site would look fine in IE 8, if it were rendering in IE 8 standards mode.
The problem is that the page is being served with a header that forces IE 8 to use IE 7 standards mode.
You can override this in your browser using the IE 8's Developer Tools. Doing so will not fix the problem. It will allow you to see that, if the page were rendered in IE 8 standards mode, it would look just fine.
What we need to do is find out what is causing this header to be sent by the server and change that. It should probably be set to IE 8 standards mode. But simply removing the header should allow the page to default to IE 8 standards mode in most cases.
Instead of messing with the custom_functions.php file, you probably should have just removed the headers from the file that was giving you the error.
What does custom_functions.php look like now? Does it have this in it:
If so, just change that to:
That will force the IE browser to use its highest rendering mode. For IE 8 that will be IE 8. For 9 it will be 9, and so on.