Webroot looks like the culprit in my case too.
Having set WR to allow taskmgr.exe (https://www.webroot.com/En_US/SecureAnywhere/PC/Content/C5_Quarantine/CH5b_BlockingAllowingFiles.htm),the PC no longer slows to a crawl when Task Manager and Firefox are open.
To see whether the problem relates to the Webroot Filtering Extension in Firefox, I tried enabling it and disabling it. Didn't affect performance with TM open, so I assume that 'allowing' TM in Webroot is the step that matters.
I'll try Chrome later and report whether the WR fix holds good for it as well.