It sucks, and I'm not going to lie about that. Most of the folks here have encouraged you, that's good, and it's what you need.
I'm not going to do that, though, and I acknowledge that I'm going to sound like a dick here, so skip to the last paragraph if you want the feel-good bit.
Your car crapped out and you have no career? That sucks. Rely on public transport for a while. Get a shitty job working minimum wage to cover your bills and put a bit away. Live within your means. If that means shit-tier Internet connection, Pay as you Go phone with restricted texting, no TV, and no gym membership, then that's what you do. You gotta man up and make sacrifices if you want to get out from under the rock you've found yourself beneath.
Your lady (who you've been with for a month? Ish?) is ignoring you? You haven't been with her that long at all and, barring any sort of bolt from the blue, love at first sight situation, it's not really that big a deal in the grand scheme of things. My wife of 10 years just filed for divorce. My buddy's wife of 9 years is sleeping with his best friend. Relationships go south. Sometimes they can't get fixed. If she won't respond to you, there's not much you can do. Don't pin your happiness on another person.
Your parents are splitting up? That's harsh, but at least they're still alive, and at least they're not using you as a pawn in their divorce.
You can't be a cop? Probably for the best, considering how you're dealing with the stress of the other stuff going on in your life right now. Wait a year. Get better, stronger, and smarter. Retry. Get in.
Your dad's depressed and suicidal? Don't just sit around and be sad about it; call his Union Rep and explain what's going on. I will pretty much guarantee you that the PD has a shrink that he can go to, and they will do it discretely, so that his pride isn't hurt.
Your dog is dying? That's terrible, and I genuinely feel for you. Cherish every single second you have remaining with it. Remember the good, and remember the bad, and remember the love you feel for it.
It seems like life is shitty now, and it is. The shitty thing is that, in my experience, it doesn't really get better. Seriously. Things are shitty even when other, better things are distracting you from that fact. Yes, you can choose only to wallow in the shit that life hands you, but you can also accept the fact that not everything goes the way you'd like.
That being said, though, do not ever give in to despair. Do not ever think that your life is terrible and pointless. You mean the world to dozens of people, even if you don't realize it or think it. You are the rock that someone relies on. You are the joy in someone's life. You are the reason why someone goes home at night happy. They might be someone you've never even met, but I can guaran-gods-damned-tee you that they exist.