For example, I've been buying $20 to $50 worth of BTC every couple of weeks since early this year, and I'm still at 0.3 BTC (or about 0.25 BTC excluding altcoins). I also got about 0.02 BTC from the PD faucet, and a tiny percentage from other faucets like Freebitco.in.
In 2009, it would have taken seconds to minutes to reach 1 BTC. In 2010, maybe a couple of hours. And in 2011, perhaps a day to a week depending on the month. Generally, how long do you think it would take for a person living today to reach 1 BTC? 10 BTC? 100 BTC? (heck, is that even possible now?)
Your question is really hard to answer and the rest of your post confuses me even more.
If you have 620~ USD, it takes a second to obtain a btc. You simply buy it.
If you're going to rely solely on faucets - you're looking at years of work.
If you're mixing faucets, buying, earn sites, signature programs, gambling, freelancing - it's impossible to say how long it's gonna take -you- to earn a bitcoin.
You can always try cloud mining, it's an investment so don't do it if you can't afford to invest, but after you break even it's a passive income.