In the US, Getting a credit card is as easy as it gets as far as dealing with financial institutions. You just need proof of residency (shouldn't be hard to get, I mean you love some place already -doesn't have to be your own place), your SSN and employment/student status. Note you don't even need a credit history. You can still get a credit card.
So do your research. If you haven't gotten a credit card and you've tried for over a year and a half as you say, you are probably doing something wrong.
If you just want to be able to buy stuff online, go buy gift cards at Walmart.
In Mexico, where credit cards are expensive and most people don't have one, you can pay most of online stuff at convenience stores. Stop whining and go work on something that solves the problem instead of expecting others to solve it.