This lady is a poet. Seriously, I remember my call center days as a Customer Service Representative and my first irate call- a verbally abusive woman who called me every name in the book- believe me, we CSRs should be given credit for dealing with these less-than-subtle people on the phone.
When I handled my own team, I also got to handle even more atrocious callers (as a rule, CSRs who cannot handle such a call must transfer to a manager or supervisor), but eventually I got used to dealing with them. I told my team:
1. These people are irate for a reason- they've experienced bad service, or have been severely inconvenienced, or perhaps they are frustrated, or simply bitches by nature (excuse my french) but the point is, allow them to verbalize and try to probe what the problem is about. Apologize sincerely and assure them you'd do your best to help them.
2. After your assessment, if you think there's nothing you can do to help his/her problem explain how it works (some protocols need to be followed, and sometimes a specific department cannot do something to augment a certain problem when the problem is, for example, technical- only the IT department can fix that). If they are still irate and you feel that the call could go on and on with no resolution, transfer the call- but don't drop it or cut the caller off! (No matter how tempting it is) You'll put your job in jeopardy by compromising quality.
Sounds like the CSR here was eaten alive by our "poet". Dead air, inappropriate sidetalk- in the end it is the CSR who will be evaluated, not the caller. Final advice: put yourself in their shoes and be genuinely interested in helping them despite their hysterics. They are people too, and it is your job to help them out. Psychos or not ; )