/sbin/resolvconf (the binary) was probably installed automatically as a dependency of another package you installed.. e.g. nscd or dnsmasq.
Whilst the main package, e.g. dnsmasq may have been removed, sometimes the files from a dependent package, e.g. resolvconf, remain.
EDIT: It looks like that is what happened when you installed dnsmasq. resolvconf is listed as a "suggested package" to install with it..
It seems that resolvconf is provided by two different Debian packages.. one package is called resolvconf and another is called openresolv.
Since resolvconf (the package) is not installed on golfer's machine, the finger of suspicion points also at the other package, openresolv.
All a bit academic now. Glad you got it sorted. The Linux Mint forum might be a better place for these questions.
Hi again..............just when you thought I'd gone away....................
As you may see from my reply to Peter on the post "static ip address and virgin media", things didn't quite work out so I'm basically back where I started! I'll keep having a tinker and see if I can get the files you quoted removed. If not, then a re-install looks the best bet.
I've posted a few times on the Mint forum (US one) but the replies are few and often take a long time. The Linux UK site, I believe, has had some issues and has had to be re-set, losing a lot of information.
Asbokid, you're definitely a genius and the pint is yours! I removed completely resolv.conf through package manger and my connection settings worked immediately. Openresolv had not been installed.
Funny how some things are simple innit..............but only when you know how!