Given an Ubuntu 14.04 server setup on a popular VPS provider hosting a single website with Nginx, Apache and WordPress / PHP, after starting the server it works fine for a while. Days later the VPS provider shows the server as pegged at 100% CPU utilization, SSH access no longer can connect ( times out ) and the website became inaccessible. Before the server went to 100% CPU utilization the server could be accessed via SSH without issue. There's also little to no load on the server which would cause any CPU use - Typically CPU use ranges under 3%.
How can I diagnose which process is causing the sudden spike in CPU use without being able to shell in? Currently, when this occurs the server is rebooted and then it runs fine for a few more days. Of course, a virus or other malware is suspected although ClamAV didn't find any potential viruses.