It's very possible, but expect to work long and hard (24/7 for a couple of years) to get anywhere. I started a pc business in the same way; with little knowledge, just out of circumstance.
Ignore the hell out of people who say you shouldn't. If you shouldn't, you'd already be sure of it and you wouldn't post here. If nobody ever pursues the 'impossible' nothing will happen and we'd all be pretty pointless. Not that starting a web design business is going to change the world... Although it
might, but there's no point thinking about that and things that 'might' often don't. You'll gain a lot of very valuable knowledge and experience no matter what. For me, a lot of things that seemed impossible 2 years ago turned in the biggest pieces of cake ever.
Oh, and here's a free piece of very valuable info: Like me, you'll automatically become a geek in the eyes of all the people you're attracted to because you sit behind a computer a lot.

This sucks, but they're right. You have to be very self critical and keep your social skills up to scratch. Don't be an actor though! People pay a lot of money to geeks with a nice personality because they are very rare and everyone will think you're some kind of insane talent. Sometimes I pull this off and when I don't, I feel horrible. When you're the person a couple of influential people go to to get things done you will start to earn real money.
And 'sound like a long uphill climb to me' is a pointless remark in the eyes of the true entrepreneur

If it's not long and uphill, what's the point?