You'll need the make and model number of the DVR to begin with, as there are MANY different ones out there and there is a great variation in how they do things. Some run on a Windows platform, some on Linux, many are 'embedded' - not only are there different ways of organising the video files, but there are other things to deal with too such as encryption, codecs, multiple HDDs (and how they are written to) and so on. If I had this job personally, I'd be hoping for no encryption and then looking to recover and sort the video files by 'Created Date', hoping that this would at least give me a chronological video list. VLC is your friend for playback. I think I'd be giving up on trying to present the videos all neatly stitched together and in a day-by-day format, as this would have been a function of the failed DVR's software.
DVRs are tough. May the client be happy they're at least able to play the video files you've recovered - not everyone is as lucky!