WP causing crazy CPU loads, site downtime and slow page loads

We have recently migrated our site to the wordpress platform. We are on our own servers. 4GB RAM. Currently getting 7k-10k visits per day. We have recently doubled the server size from 2GB which has decreased the amount of downtime on the site when the server load goes crazy. But the server load is still temperamental. Using version 3.8.1

We have a number of issues which may be due to a single problem which we can’t work out.
The main issues include:
– High CPU load when publishing activity and traffic is high (we publish 10-15 blogs per day) causes site downtime.
– CMS/admin page loads are always slow (6 second page loads)
– Due to the URL structure we have two pages that display the homepage blog content. One at ‘domain.com’ and one at ‘domain.com/blog’
The ‘domain.com’ however does not update with the latest posts and can take up to a week to show the latest content.
– We have the cacheing plugins installed (w3 total cache)
– We get signed out of WP when saving updates to plugins, disabling plugins and deleting plugins.

We have deactivated plugins etc but nothing seems to work.

Any advise or ideas of what could possibly be causing these issues would be HUGELY appreciated!

Thanks