I would upgrade your site like bryantrv has suggested it does resolve a lot of known exploits. Also, I would add a comprehensive .htaccess file where you can block the offending ip addresses and known exploits. I have posted an abbreviated example of an .htaccess file that you can have a look at. it is located here
http://www.lunarforums.com/lunarpages_security_center/example_of_an_htaccess_file-t53352.0.html If you have any questions about it. I'm always available for more help. The section of known exploits will have to be searched on the Internet an added manually as they change almost on a daily basis. It is a good starting point, and will help, but no guarantees that it will help keep all intruders away. It just acts as a firewall. Since I implemented my .htaccess file I have not had any weird bots or the offending IP addresses visiting my websites anymore!

I'm also more diligent in keeping on top of the scripts that I run to make sure that known exploits are patched immediately. I run Linux as my desktop, so running anti-virus, and malware is not as important, but I do anyways.
I would do everything that has been suggested in this forum, and Backup your website once it is clean to your computer, it is much easier to restore later on.

Cheers!
eTech97