Faucets is probably the worse way you can "earn" a little bit of bitcoin. Anything else using your computer's computing power (you mentioned keeping your browser open) is also a bad idea because as CPU mining has been unprofitable for over 18 months now.
If you have any kind of coding or similar computer skills I would recommend going to the marketplace subforum (services child board) to try to find some kind of work that you can do for bitcoin.
No coding skills :/ just a man on a mission
What other skills do you have? When you need money, how do you usually go about earning it?
If you are looking to sell digital goods, some suggestions would be things like airline miles, gift cards, rewards points. It would generally not be a good idea however to use fiat to buy these things so you can get bitcoin because these types of goods will usually sell at a discount when exchanging them for bitcoin so you would be better off buying them on an exchange.