I have a similar issue with my drivers door on my 1997 accent. Hence why I am here. I have found the mechanism within the door panel seizes up and in turn has put pressure on the catch behind the handle on the inside of the door. Twice I have removed the internal panel and eased the seisure at the door mechanism which helps in the short term. This may help, but what happened to me next may be your underlying issue. When i was re-fiting the interior handle after the second time, the little white catch that links the pulling of the handle to the movement of the rod to the mechanism snapped and now it won't work. I would suggest one or both of these issues would be your best bet to investigate for now. If I resolve my issue with the broken catch, I will let you know.
Dave (Glasgow), March 2009