What is a good job at a startup for someone who is passionate about mobile product, but isn't technical, has a good eye for interaction design, but isn't an proven designer and has 1.5 years of support and product QA experience, but doesn't want a career in support?

You have lots of options as listed here.  It can be hard to work in a startup if you lack experience since most startups tend to hire for actual skills not potential.  One option, if you can afford it might be to work for equity in a startup on the side, while taking a day job to build your resume.

Look at kind of companies, they encourage participation of people with great passion and innovation for design.

I think you should invest in yourself to build skills. If you dont want to go through the long cycles of growth in corporate world its better that you wait and do a program or two, Be it technical skills or management skills. Look at product marketing and Pre sales kind of roles thereafter!!

If you are willing to be flexible on terms, time and compensation, you can try out with some startups and see what you really like to do. I have created a platform just for that http://ekwity.com. Check it out.

If he's still asking this question to himself. He's not good enough. These are rare traits which is difficult to learn and quantify, nor you can quantify/learn passion nor you can develop good taste.

If you don't have any specific super power, and you don't want to continue working in the only thing you have proven experience with, the real question is "for what role should a company hire you?" Generally speaking, Companies hire people to solve specific problems they know they have. If you don't know what specific solutions you can offer, it is going to be hard to find a good match.

Others have mentioned this above, moving into Product Management may be a good progression from support to consider particularly if you have limited technical skills/experience but have good business analytical/communication skills to offer. Having worked up from a support position to becoming the eventual Product Manger of the product I originally supported. I found that having a constant enthusiasm and passion to improve the product further got me to my current position. I also communicated regularly and absorbed information throughout the various teams, which will get noticed in a good company. From reading from other peoples experiences, Product Management as a role varies at each company (and sometimes even by product!). I'm very fortunate that I work in a small team, so that I can be involved in some UI design work, even if not in a dedicated role.

You can try looking for entry-level positions. For example, the company that I am working for, http://www.vericant.com/hiring/, has an Operations Associates program. It is targeted at people without extensive professional experience, and it sort of a training program.

Personally I am believer in learning things on the job. If you have the passion you can learn a lot of things quickly. While it is unlikely to start of as Product Manager directly, it is important to make the jump to the product side of things and work your way up.  Smaller startups, just at the stage of starting up / establishing themselves always have a need for people who can play multiple roles. Getting in is the toughest part. Work your way in using references to get interviews.