It sounds like it began as something like teeth but has now become a bad habit.
When my daughter was a baby we did the following (religiously) :
First, we had a 10 minute rule in our house - we would go into her only if she cried for more then 10 minutes - and only if through those 10 minutes it was a constant screeming cry (not just a snuffling and moaning cry - in which case we would not go into her (although I used to stand by her door very quietly and listen (as worried mummies do)))!!
When we did go into her we would NOT turn on the light and we would NOT give any eye contact at all, we did not talk to her, and if we ever did talk it would be in monotones : "sleep time now, go to sleep" - but tried to avoid talking at all really.
We would check her nappy - if full would take her out and change it - still no lights (not easy but doable).
We used a dummy so if it had fallen out we would put it back in her mouth and walk out. If that did not work we would pick her up and hold her until she stopped crying - as soon as she stopped crying we would put her down straight away and walk out (at the start we would have to do this several times - the key is not to hold baby when she stops crying)
I think it is important to make baby aware, through your actions, that this is not a time for waking up, it is a time for sleeping, and not giving her stimulation helps with this.
Within 2/3 days she would be back to sleeping through.
Consistency has always been key as well - and not giving up - it WILL work, and it is NEVER too late to try ...
Good luck, hope it works out for you poor exhasted parents
