There's a condition (which, incidentally, I suffer from) called
Central Auditory Nerve Processing Deficiency.
Essentially (As far as I can recall) the brain tells the ear what to hear as much as the ear tells the brain what it's hearing, and this level of pre-processing (or some of it) occurs in the central auditory nerve. If there is a defficiency in this processing (the problem from which I suffer) this can result in the situation where an individuals peripheral hearing is good, in a quiet environment they here everything that everybody else can (in my case, my peripheral hearing is actually above average - I hear things about 90% of the population miss), however, you get them in a noisy environment, and they are unable to discriminate words because of the background noise.
The extent of this can vary from simply mishearing words (hearing bat as cat, for example) to simply not hearing people (or other noises) at all (effectively being clinicly deaf).
As I recall, the results of the last time I had my hearing tested showed that although my peripheral hearing as above average (I tend to score very highly in single tone tests) at anything over something ridiculously low like 20%-30% noise i'm pretty much clincaly deaf - this causes substantial problems for me at home, for example not being able to hear my wife in circumstances where I should (go ahead, yuk it up, sometimes she forgets), I find it very hard to carry a conversation in the morning tea room (or at a party- people often mistake me for an introvert when they first meet me).
This is more complex then 'simply' bad hearing, on many levels, for example, when I attended university, I couldn't study in the library, because I was unable to filter out the infrequent background noise, every cough or sneeze had my instant and full attention, because I couldn't ignore it, I found it far more effective to study in the cafeteria where there was constant background noise which became like static. It also means that I have to turn the television or radio off completely in order to carry a phone conversation, because i'm completely unable to focus on one over the other.
It also caused no end of trouble for me in school, because my teachers knew I had good hearing, and attributed my lack of responses to them as being the result bad behaviour rather than an inability to discriminate their speech from background noise.
Being tested for auditory processing deficiencies is possible (I think the wikipedia article meantions HINT, for example), however, as I recall from my own personal experiences hearing aids are virtually ineffective (when I was 11 I was involved in a trial of a new system involving an FM microphone and a recieving unit, however that created other problems regarding sensory overload).