Translation:They could not open the door from the outside.
Here is a simple check: when there is "kein" in German, you can use "no" in English. It does not always sound well, but it usually works. Like: Ich habe keine Babys - I have no children. Ich will kein Kleid - I want no dress ("I don't want a dress" is maybe better, but "no" also works). "Kein" is much more common in German than "no" in English.
"Kein" is always used with nouns and "nicht" with verbs.
In this sentence you could probably use "kein" with "Tür": Sie konnten keine Tür von außen offnen", but this would mean "They could not open any door from outside" (They could open no door from outside).
These are my own explanations, please be aware that I'm neither a native German nor a native English speaker. See more about "nicht" and "kein" here: http://german.about.com/od/grammar/a/German-Negation.htm