Jamba, I'm guessing you got into teaching originally either because you like teaching itself, or you like working with kids (or possibly both). If it's just the former, then you could consider moving into adult education, or possibly into training (I know a couple of people who work in IT training who originally trained as teachers). If it's just the latter, then there are a lot of related jobs (you probably know better than me, tbh) - Learning Coaches, SENCos, Careers Advisers, etc. Being trained and qualified as a teacher will prepare you for those careers, but unfortunately they'll generally require further qualifications. If you are still training, I'd suggest giving serious consideration at least to completing the qualification - teaching qualifications are relevant in a lot of other career paths, so it won't be time wasted, even if you don't want to be a teacher.
I know a few folk who are teachers (or former teachers) too, and the school you're in also apparently makes a huge difference. If you're not happy, it might just be the school that's wrong, rather than the career. If it's being in a state school that doesn't agree with you, you could also consider moving into private education, special or alternative provision (e.g. special schools, home tuition, traveller education, pupil referral units).
Regarding looking at your strengths and weaknesses, as Mr Monster quite correctly says there are a whole load of psychometric assessment tools available. Access to those tools can be difficult - some of them you can complete postally I think (there is usually quite a hefty charge). Your best option might be to see your local careers service - if you live in England it's an organisation called Connexions I think. In Scotland it's Careers Scotland (http://www.careers-scotland.org.uk/) and in Wales it's Careers Wales (http://www.careerswales.com/).
There are a few online tools that may help you - http://www.careerswales.com/adults/server.php?show=nav.2950 has a search tool that'll semi-intelligently suggest career paths based on your preferences and skills (even if you don't live in Wales). Ultimately though, although people and assessment tools can offer you suggestions, it's only you that'll know the perfect career for you - you just might have to try out a couple of duds first.
What makes me happy in my job... being challenged, and meeting that challenge. Having the opportunity to be creative. Interacting with nice people. Having the time and opportunities to develop my skills and knowledge. Good coffee. Flexible working hours. An informal work environment. Respect from colleagues. A supportive team. Guess I am pretty luck, when I look at it.
Good luck with your search!