This task is not so trivial as it sounds: a punctuation character is intrinsically context dependent.
E.g. the dots in at the beginning of this line do not make a sentence each. ;-)
Or "(see item 1. above)" does not terminate after the dot.
There is many more cases also with other punctuation characters.
But it looks like this is not the topic of the question.
So, if you want to simply get the chunks of text between some delimiters, treating repetitions of delimiters as one delimiter, stripping off leading and trainling spaces from the found chunks of text, then the following would do:
string fullText = "...";
char[] delim = ".?!;".ToCharArray();
var sentences = fullText.Split(delim, StringSplitOptions.RemoveEmptyEntries).Select(s=>s.Trim());
foreach(var s in sentences) Console.WriteLine(s);
Cheers
Andi