How about small laundromat start-up?
What kind of business would keep you interested? Do you speak a reasonable amount of Spanish? Would you be willing to work 50-60 hours a week or more to get it off the ground? For that kind of money, you could do business-to-business distribution. Many small business owners simply do not have the time or resources to get new products, but if you can find something they could mark-up more than 20% while making a decent profit yourself, you should be able to sustain yourself.
One of my first ventures was baking cookies in a very small commercial oven on a Pacific island. The oven I used was $1500, a Kitchen Aid Mixer for $350 and a $100 dorm fridge--less than $2000 total. After it took off, I was producing some 2000 cookies a day(200 cookies an hour from scratch for 10 hours), three times a week. I distributed the cookies to about 50 small stores on the island in boxes of 60. The stores made 5 cents a cookie and I made 8 cents a cookie after food costs. So at 6000 cookies a week, I was netting about $450 before expenses which was more than three times what the locals would normally make working full-time.
===
If you can get products directly from someone who imports, you can start developing your own distribution business. Eventually, you can learn how to jump through the import hoops and find someone abroad who can fill barrels of product for you from say NYC and you can then vend them. I knew one guy who made a very nice living just selling Chinese knock-offs of American diapers. There are many products that if you can import, you can double your money on them. Another person I know sells spices to restaurants and now grosses well over a million in sales every year and they also started small.
In my experience, the more boring a business sounds, the more likely there is a profit to be made from it. It's also easier to find something that is needed and meet the need, rather than creating a new business and then finding a market for it.
===
Another venture would be to import some cheap coin-op video games, just not gambling ones. In the US, the deal is you put the machines on a bar countertop and every two weeks or so, you stop by and split the coins with the bar owner. It accepts US bills which are not hard to come by. I know a bar owner who bought one of these(no splitting quarters) for $400 on Ebay and he says he gets about $5000 a year on it-- on ONE machine.
Working Merit Megatouch MAXX Ruby 2 Touchscreen Bartop Arcade Game | eBay
Of course, you'd need some kind of security agreement with the bars in case the machine is stolen or gets smashed...