Would it be considered cheating to ask for homework help on the internet, if I openly acknowledge the help received?

This depends a great deal on the professor and course in question. Better to ask first if you plan to do this. Also, check the syllabus if there is a stated policy regarding help on homework.

I think it is acceptable, but you might considering asking your professor first.

I have cited help from cross validated and stack overflow before with help on modeling in R. I tested my data for heteroskedasticity using a test (Breusch–Pagan)that the professor did not mention in class.I provided a link to the discussion in my assignment. I did not receive negative marks, in fact, he actually complemented my work in front of the class for "going the extra mile" and using alternate resources and finding a test he did not mention in lecture.

I think most professors want you to learn, it shouldn't matter how. Now if you post you data and someone does all the work for you, that is a different animal..

I would say that it also depends on how you asked your question online. You should demonstrate in your homework that you have understood the procedure you're outlining as your answer, and then acknowledge that you received help online by providing the link where you asked your question. If I were the professor, I would click the link to see the question. If it were a question along the lines of "Here's a problem. What's the answer?", then I would give you no credit. If your question clearly showed some effort and understanding, and that you made sure you properly understood the answer(s), I would say it's ok. But most importantly of all (I think), you should admit in your question that you're working on a homework problem. That way people will try to help you rather than just give you the answer.