I would continue in your computer science studies but make marketing your hobby. Perhaps look for a freelance jobs you can take on for a marketing department.
As far as interviewing, talk about marketing being your passion... talk about the benefit of a marketing person who can interface with computer scientists and speak the same language.. look for a company that markets to computer scientists and you will be " in like flint".

I agree with rbauman on the strengths of your customer support experience, but it would also help to make sure you've covered the basics of marketing concepts and techniques. You can do that by reading on your own; you might also decide to take classes.

From the little info you've provided, it's difficult to offer much advice. Obviously, you need a well-tailored resume which shows how your experience and education makes you a good candidate for a marketing position. Perhaps you can find a computer or technology-based company who will appreciate your knowledge. Writing and speaking are big parts of any marketing position, you'll need to make yourself shine in these areas to even be considered.

Good Luck,
Debi Brady
Writing & Marketing Consultant