Sometimes problems are not fixable, I get that. War torn countries, toxic environments, friends or maybe even family that actually drag you down rather than help you up. If you've searched and searched for a solution and you simply needed to leave your home country and everything you had for the sake of your well being, then I commend your strength and resolve - many people in your situation are simply too scared of the unknown to take that leap.
Here's the reality check though. There is no land of opportunity where you can run to and rely on an honest hard day's work to get you a new and steady life. If there was one, Argentina definitely isn't it.
If you want to make it with a fresh start in any country, you need a lot of things. Planning and backup planning, resourcefulness, a support structure of some sort, relentlessness, a good amount of time to implement your plans, etc etc.
If you have already decided on Argentina, and there is no going back, I would start by analyzing who you are and what you can offer. You seem to be a programmer. My advice would be to spend the next year learning Spanish and continuing to develop your programming skills. Take as many projects as you can and live on as little as possible to create a good savings account. Research the Argentine industry for the types of programming jobs that are most commonly sought after and learn those programming languages. Become someone that you could see these companies hiring, or contracting. Create a portfolio so you can showcase your work somehow. Start networking with people in the industry here via LinkedIn and other social networking channels. Ask a lot of questions, send emails, make contacts. Try and visit Argentina at least once during this time to get an idea of what you're getting into, and so you can meet people and begin to create social and professional circles. Learn about the economy here, learn about the culture, the people, the way things work on a daily basis. After you've done all this, you start looking like someone who could be ready to move to another country in search of a new beginning.
I hope you understand my point - its similar to many other posts above. You haven't given us enough information to provide you with specific advice, but its clear you've decided you need to move and you want to move to Argentina. Rather than asking the forum members about the intricacies of the web programming industry here, or how best to learn the language before moving, or the average rent prices etc, you've just said you're at a breaking point, and that you are so hardworking you just want someone to give you a chance in Argentina. That is a big red flag.
Get started on a plan, and I'm sure people here will be more than willing to share their insight on your plan and what it needs and doesn't need.
Also, on a more personal note - if you actually are situationally depressed, I hope you've sought help with that. Situational depression is something caused by a traumatic life event, and its a tough state to be in. With the right support however, you can climb out of it, slowly but surely. There are a wide range of remedies that can go a long way to good mental health, and I hate to say it, but moving countries without a plan is not one of those remedies. Argentina won't cure your depression. From someone who knows first hand about depression, I really urge you to get help and fix or stabilize that condition before thinking about a big life change like moving.
Good luck.