If that is the same site I looked at a couple of years ago, the site is probably not corrupted. You very likely have a conflict with some of the plugins or your theme is not compatible with current versions of WordPress.
Andy is correct. The core code should never be modified. Technically speaking, the only code that is modifiable is the theme or a custom plugin.
Have you tried updating WordPress to the current version? If you have and you still have the problem, make sure the plugins are all updated. If that doesn't fix it, try disabling each of the plugins one at a time to see which one might be causing the problem. If none of those steps identifies the problem, the issue is likely an incompatible theme. It is not unusual for old or poorly coded themes to be incompatible with newer versions of WordPress. If it comes down to that, try a new theme. You can always switch over to the TwentyTen, TwentyEleven or TwentyTwelve theme temporarily to see if the admin problems go away.
I'm involved in an intense training program for the next couple of weeks, so I cannot take a look at it right now. However, it shouldn't be scary if you follow the steps I gave you. Plus, you can keep your $60 in your pocket.
"Democracy is two wolves and a lamb voting on what to have for lunch. Liberty is a well-armed lamb contesting the vote." -- Benjamin Franklin