Translation:I will not go to school because my head hurts.
頭が痛くて、学校に行きません。(I have a headache and I won't go to school.) ~くて (with い-adjectives) and ~で (with な-adjectives) is the "and" in a sequence of events (I did "X", and/then I did "Y" or "X" happened then "Y" happened). The て-form of verbs functions in a similar way for sequence of events. 例：今朝、午前六時に起きて、日本語を勉強しました。(This morning, I woke up at 6 and studied Japanese.)
頭が痛いので、学校に行きません。(I won't go to school because I have a headache. ) ~ので (following い-adjectives and plain form verbs) and ~なので (following な-adjectives and nouns) mark the reason for why you did/didn't do something or why something did/didn't happen. It's something like "so" or "because". It's similar to ~から but tends to be a little more formal.
Happy studying! :-)
I'm confused. The translation on the discussion page says, "I won't go to school because I have a headache," but it marked, "I won't go to school because my head hurts," as wrong, saying I should use don't instead of won't. In an earlier sentence it would not accept "I have a headache" rather than "My head hurts" for あたまがいたい. I assume they just haven't yet added every possible English translation combination to the list of acceptable answers?