however, yes the demos helped considerably... its a very strong proof of knowledge and skill. a working demo of reasonable complexity is worth more than any level of academic background or past experience outside the industry imo. you just need to get it seen.
as a programmer i can't really offer much advice for design, art or production though. i imagine design and production is basically luck or attitude to get into - everyone wants to do it and the skill is difficult to measure. artists tend to have impressive portfolios and/or showreels demonstrating past work and personal projects...
A surprising amount of production staff have a background in the QA department in my experience too... QA is definitely a way in for all the disciplines but I have no experience of how that works well.