I purchased 2 roundtrip tickets for my inlaws at $250.  My father in
law became ill and could not make the outbound flight.  He drove with
his wife later.  We asked the gate attendent if they could use the
return portion of their tickets, and we're told it would be alright. 
When the return flight was attempted we were told that the airline had
cancelled the tickets.  The gate attendent told us that all would be
ok.  He would sell us two new one way fares at  $750 and that the
airline would refund this purchase.  Upon returning the airline said
no-way.  What recourse do I have?  Who should I contact since the
airline basically has a unique system of of allowing only one way
communication in the customer service department.  The airline is
American Airlines.

You fell into what the airlines call a "hidden city" ticket.  For
example, I might want to fly to St. Louis, but the flight costs $400
nonstop. The same airline might have a flight that goes through St.
Louis, utilizing that very same nonstop $400 flight, to Denver, for
$300.  It's very tempting to buy that Denver ticket and just throw
away the second ticket, but you could only try that on a one-way-- on
a roundtrip, they'll cancel the return flights and you're SOL.  The
airline assumed your in-laws were trying to pull that stunt and thus
cancelled your tickets.

You could file a complaint with the Better Business Bureau if you want.

While keystroke was almost on the right track, your case was not a
"hidden city" issue.  Sometimes in airline pricing a roundtrip might
have a lower fare than a one way ticket. Therefore, some people try to
buy a round trip with the intent of throwing away the second (or
first) segment.  To prevent passengers from doing this, airlines
always cancel a return if the outbound is not used.  This has been the
case for years and either the gate agent who told you otherwise was
lying to prevent a confrontation or you misunderstood.  Either way,
these are the rules that passengers must abide by when using the
airlines.  If you have the name of the person who misled you and some
proof or witness that they misled you, the airline might give you a
credit just as a customer service, but I would not count on it.  It
doesn't hurt to write a letter to their complaint department though.

Over the years, when I've felt frustrated by airline service, I've
written letters of complaint (hand written and sent via postal
service) to the airlines (different ones on different occasions). We
have *always* been well compensated by the airlines--free tickets,
etc. I highly recommend you take it up with them and see what comes of
it. I can not think of a single time that they did not respond with
*something,* usually something quite nice really.

Sincerely,
Boquinha-ga

boquinha-ga has a good point.

Airlines work by selling the majority of their seats at low prices,
and ripping of anybody who is desperate.

They also don't like bad publicity.

Start nicely, and get nastier, by the time you are using GA to drive
people to your web site describing what a bunch of xxxx they are they
will give you a first class round world trip.

This sounds like a cockup, at a very low level, but it is worth pursueing.

Document every step, record telephone calls, you could find this rather amusing.

Keystroke and Research-help describe the situation correctly.  I
wonder why the "scam" hasn't been challenged in court: what right does
an airline have to reneg on a contracted ticket  - and not refund?