I know exactly how you feel. You just need to take it in small steps, and you'll be able to escape your funk. Think of it as walking before you run. Since I too, am too broke to join a gym, I started lifting jugs of water, just make sure it's sealed haha, I once lifted a jug that I had opened earlier that day and I ended up with half a gallon of water all over me and the living room. I usually do it when I'm watching tv, I started out with one, lifting it above my head on my left side with one arm or both, then I'd switch to the other side. I only did this for about 5 minutes. Then I walked in place for 5 minutes. If you do this 3 times a day, you end up exercising for 30 minutes, without having to leave the house, or change out of your stretchy pants, and without having to shell out money for a gym! Eventually you can move on to two jugs, and walking longer in front of the tv, until you're able to go outside again

I lost fifty pounds just by finding a way to move around in my apartment during the winter time. You can do it!
As for the food, make gradual changes! I used to eat only cheetos every day and energy drinks, but now I don't even drink soda. If you like chips, switch over to sunchips at first (they're whole grain and lower in salt than the usual kind of chips, helps with bloating and that tired feeling you get after you junk out). Change your white bread products to brown, sneak some frozen vegetables into your diet. Try to always make sure you eat breakfast when you get up, so you can avoid oversnacking. Realize that you're still going to want some junk food here and there, but try not to buy as much of it. If it's not around, you can't eat it
Most importantly, just understand that you're human. It'll take time, but just by thinking about how you can get started, you've already gotten started!