the same thing kinda happens to me..definitely not as bad as you, but after running for 5 seconds i get faint and dizzy. probably due to the fact i recently went through a period where i was severely under eating, and over exercising, i used to be super in shape, then i stopped exercising for only 2 months and bam now i rarely can get into a good exercise regime.
anyway, i find its best to slow into things as much as possible. I would advise you to seek advice from a cardiac professional since, you have health issues, you wouldnt want to jeoprodize your health trying to exercise. Ask them questions about good exercises to do that are well suited for you body. I cant make up for actual medical advise, but due to my old exercise obsession, I do have some tips and health advice in easing into exercise.
Cardio: The only way to increase cardio health is to keep doing it regularly. Id say in your case, once every two days, due at MOST 15 minutes of cardio. Since you say you get nauseous, try interval training. Do slow jumping jacks until you start getting uncomfortable and notice that you probably should give yourself a break (i mean way before you get to the nauseous point) Then stop, and breathe in and out, in and out. Have some water. Wait a minute (or until your heart rate is back to normal) Repeat the jumping jacks until you get tired again. Take a breathe, breathing in and out, and wait until your heart rate is back to normal, and repeat five times. I usually run in place instead of jumping jacks. I used to be able to run 3 miles, now i can barely deal with one lol.
Also, the thing about cardio, is that it isn't as important as magazines and health tv gurus make it out to be. Yes, it does contribute to weight loss (but your diet contributes more) But OVER cardio training is bad. In fact, you should never do more than 40 minutes of cardio at a time. When you do this, your body starts stressing out and releasing cortisol, etc, and over time your body will burn out. Balance is the key. Weight lifting, is fantastic way to do cardio and strength. Im very weak in the arms, so I can only do at most ten push ups. I recommend doing 5 push ups to see where your level is at.
And if you find yourself sitting down for long periods of time, just get up and stretch. Do some yoga. Im serious, just try to touch your toes, and do some sit down back twists etc, stretch your arms. Another thing that contributes to poor physical health is not keeping your muscles and bones feeling nice. A long day of sitting down will make your back ache and make it harder to get into exercise. For every hour youre sitting down, get up and stretch your legs. I do this at work, I dont care if its weird Id rather not go home feeling tight and lazy. Also siting down for long periods of times makes me tired, I get to the point where i want to sleep. Getting up and giving your body a time to move will give you more energy.
Instead of jumping into a sport just try doing short easy exercises. Due to your current state, doing little spurts here and there will help you condition for the future when your doctor thinks its okay for you to do more intermediate exercises. Id say squats, jumping jacks, push ups, leg raises and any stretch is in safe territory for you. The reason I say this is because I don't know your current medical condition, SO i dont know what will be totally good for you, I am only judging by what you wrote. Don't do anything strenuous, and take baby steps. Many mistakes people make is jumping into fast into anything, which can result in injury.
But I strongly advise you to see your doctor and ask them first, they know your physical health, not me. Those little disclaimers about asking your doctor before starting any exercise is true, especially if you were recently injured. Being inactive for a long time will make it harder to exercise, but I am worried about what you mean when you say really bad. I also advise you avoid any caffeine or stimulants. It will give you energy, but its not good for the heart.
Also of course, diet. The most simplest advice I can give you is minimize fast food, processed foods. Cut out the obvious junk food (sodas, mcdonalds, chips, candy, greasyness, etc) Drink plenty of water. If you cant afford to buy fruits and veggies, try frozen ones, those are totally fine. I think the latin way of eating is both affordable and pretty healthy; rice beans and chicken, with of course vegetables. Buying rice in bulk (prefferably brown rice) and beans will provide you with good protein, and from what I know these run in low prices. My whole life thats what my mom fed me and my family. It also tastes good so you wont be eating boring veggie foods. But of course its difficult to change your diet and it will take time. If you have any questions feel free to ask me.