Our hosting Liquid Web is going through this now to figure out the best solution to this.
We uninstalled W3TC plugin with the extra files and it wound up taking our server out (and we've got a very beefy dedicated one). They've been getting complaints of the same nature all month so they're now working on a solution that we'll share on here.
Has anyone tried reverting to an earlier version to see if that solves the problem?
What sucks is that I paid the developer (or his employee) to configure W3TC to work perfectly with my site and it appears you have to pay again if this type of issue comes up. $400 was a lot for something that only worked for a few months. Never again.