Just piping up to say that I am similar - fine with computers / electronics, but pretty hopeless with most other DIY skills.
I found the best way to get over the psychological barrier to fixing stuff is to sit down and write out what the worst-case scenario is for your fixing task. My next DIY task is sowing up some nasty tears in my favourite jeans, which I've put off for ages. Worst case is, the jeans are still rooted, and I still need to replace them. So what's to lose? Not much.
Admittedly for jobs with sizeable expenditure it's harder to justify the act. I painted the bathroom by myself last summer, cost me around $100 because I had literally no painting tools and nobody to borrow them off. I had to buy the kit I needed from scratch. Worth it? Well... it's a pretty shoddy job for $100. But next summer I'll do it again, fixing my screwups (though probably making new ones) and I won't need to buy the tools again, so the next one should be a moderately shoddy job for $50ish!
I will confess, I never worked on my own car, not even oil changes - just topped up the various fluids as necessary between services. Why? Just like you, when I still had a car I needed it to commute. Thus, screwing something up and putting the vehicle out of commission was not an option. Don't despair - there's always something you can do to improve your DIY skills.
Also, it comes with age and experience. I'm mid-twenties, and I'm a lot more handy than I was when I moved out of home at 19, though still pretty bad. My older brother, in mid-thirties, is plenty more handy than I am, but tells me he was crap at DIY until he had to renovate his house in his early thirties. My dad is very handy now he's nearing retirement age, and he tells me he learned about cars in his twenties, home maintenance in his thirties, and renovation in his forties. No rush. =)