if you have a filter for "begins with A," you don't need one for "does not
begin with B", right?
Off the top of my head it might be easier to paste a formula in the column
next to your data, and then do an autofilter on that column for your results.
Advanced filter can be a pain, in my experience.
For example, if your data is in column A, and you're filtering for begins
with A and contains C, you could do
=AND(LEFT(A1,1)="a",ISNUMBER(SEARCH("c",A1))) This formula will return TRUE
if the word begins with "a" and contains "c".
If that doesn't do it for you, let me know.