I'd think it's a definite asset because it required that you understand people, and having a background in something other than marketing means you're better connected to a broader range of personalities and mentalities. So I think that's an asset.
I found an article that has some suggestions that could help you out, especially in regards to getting additional training beyond your current certificate:
It will take determination and persistence, but it can be done. You will find that a start in marketing will normally put you in a position as a market research assistant, print buyer, general management trainee, or you can enter a program as a graduate trainee.
A few companies that offer Marketing Graduate Trainee programs are:
Mars doesn't have a specific marketing training program for graduates.
They fun a cross-functional management development program, through which graduates have access to opportunities in marketing. Recruits to the program are typically given three to four assignments, the first of which may be related to their experience or studies. The remaining assignments will be in other areas, and one may be overseas. Their goal is to broaden trainees' experiences.
Nestle has recently changed its approach to hiring graduates. Nestle recruits in a similar fashion as to how they recruit other employee levels. Each department now recruits graduates throughout the year on an 'as-required' basis. Vacancies will be posted and advertised throughout the year.
Proctor & Gamble
Procter & Gamble's graduate training program recruits graduates into one of eight career tracks, including consumer and market knowledge and marketing. Consumer and market knowledge involves sophisticated and proactive market research-based work to identify business opportunities, including new product development. The marketing function involves growing the value of brands within the P&G product range. Marketing trainees will learn about advertising, PR, consumer bonding, direct marketing and project management within their first two years. The applicants are selected according to application form, a problem-solving test, interview, and site visit, where they will meet prospective managers and colleagues.
If you decide that the graduate training program route is not for you; you can still break into the field of marketing by being persistent. You will need to be willing to take on an entry-level position in most marketing agencies and work your way up. If this isn't a problem then it's time to begin your first marketing assignment, which is marketing you using your resume. http://marketing.about.com/cs/marketingjobs/a/breakinmrktg_2.htm
I think the important thing to take away from the above is that you're probably going to need to build experience by starting out at entry-level jobs. Ideally, based on your background you should look for entry-level jobs with companies that are targeting university students. Your experience working with students will make you stand-out when looking for that job. Try thinking about some of the businesses in your area that make products or have services that are geared towards students and finding out if they're looking for any new marketing trainees.