Ive been running a small webhosting company for years now, and I might be able to provide assistance in tracking down the problem.(assuming this is a linux box )
I would need an account that I can su my way into root though so I can get a hold of what I would need starting with assorted log files. The timeouts give me the feeling that someone is running some sort of php exploit/mail injection/iRC bot/filehosting. I can't find out though if I can't peek inside.
Anyway, if you want the help (again if its linux, I'm not familiar with Windows based hosting) let me know. I'm not looking for cash, just offering a hand.