That device does not appear to have an internal harddrive or other storage medium. Any memory that would have been used to burn the DVD would most likely be a small amount of memory for buffering purposes only and is most likely volatile (All data is gone on power-loss). If this is the case, then there is no way to recover the video file from the VHS/DVD recorder combo-unit.
If I was wrong and the device does indeed have an internal harddrive, it should be shut down and pulled immediately. From there you can run it through various data recovery / undelete programs but if needs to be absolutely clear before-hand that ANY write to the harddrive could corrupt the file you want to recover. Even if the file is found, it may not be recoverable.
Typically, the harddrive has two key sections for storing files... the data, and a map (The terms used are not the technical terms). The actual 'data' of the file may be in one or more physical locations on the harddrive. The map will store this information so your files can be found. When a file is deleted, the map gets changed. The map may say nothing is there, but you can still go read the 'data' for your file. This is an easy method of recovery, as all that is needed is to scan the entire harddrive and re-build the map from scratch. However, any time something needs to be saved, it consults the map and looks for some 'empty space'. At this point it could save over top of a piece of your file because this space should be 'free'. This will lead to unrecoverable data, or complications recovering the whole file. It must also be mentioned that this is true for ANYTHING that get saved... even momentarily. For example, windows systems will automatically write a file on a USB drive to test if it can be used with ready-boost. This file only exists for a moment, but this test could damage any files you wish to recover.
It is always a gamble to recover you data, and it should always be expected that very close to 0% is recoverable. At this point anything you do manage to get is gold.
I accidentally reformatted my harddrive during a windows installation... it was a 500GB disk full of programs, pictures, music, text files... everything. This was where I put my personal files... Windows existed on a different harddrive. I used a few different recovery tools and lost a lot of my data... I think overall, I was able to recover close to 90% of my data... or so I thought. I am still finding bits and pieces of files that don't work, or don't completely load and my experience occurred over 4 years ago. I found a very good song just yesterday that played for about 25 seconds, squeaked, and stopped. So even if you can recover the file, there is no way to know if the whole file is actually intact...
