I bought an external for my old PC, but I have a new one now so I have one internal and one external! They come in handy.

This might sound like a daft question, but you are using a DVD disc and not a CD disc? Thats something I struggled with at first, trying to make VCD's instead of DVD's!
And does it make a difference if you use Nero instead of Premier Pro? Sometimes just using a different programme can help.
Otherwise, you could try splitting the file instead of cutting it, then you won't lose any. I have usea 'Easy Video Splitter' in the past and its great. Very easy to use.