Years ago I was once right where you are. 315 and I realized something had to give..same height too so we were probably exactly the same size! Anyway, I bought an elliptical and started using it at home and like you, was so out of shape, on the lowest setting, 2 minutes in, I couldn't do anymore.
So if you can only do 2 km walk, do that each day - you have to start somewhere and 2 km is a great start. Also, try using the recumbent bike for as long as you can different times throughout the day and keep pushing yourself to a new time/resistance level.
I kept going at the elliptical until I could do 5 minutes, then I tried pushing to 7.5 min. then 10, then 15, and finally 20. Then I started raising the resistance. I would do 1 to 2 hours a day broken up into 15 or 20 min sessions. I worked from home so this made that easier than for most I realize. After 10 months I had gone from 315 to 190 lbs.
I had to drastically change my diet as well which is something you'll really need to address if you want the cardio to work. If you're like me though, setting goals and tracking weight/waist size each day can be really motvating but for some people it isn't so you'll have to find what makes you motivated. If you do decide to weigh/measure I suggest first thing when you wake up (after peeing of course lol) That way you'll get a more consistent measurement. After you start eating and drinking and sweating you'd be amazed at how much your weight can fluctuate.
Also, I'm not sure if this is helpful, but I found places like biggercity.com really good for meeting attractive guys that were interested in bigger men which helped a lot with my self confidence. However, if you want to lose your weight it may not be the best thing to hook up with a guy that is only into bigger guys
Although your goal may not be 32" waist? If you only want to say, get down to 240 or something, a guy there might be the right fit?
Also, almost forgot...don't set some crazy goal - 190 for example. It will feel too far away and unattainable. When i started I wanted to get to 240...decently plump but not embarassingly so
Well when I got there, I thought whats another 50 lbs...I'm going to keep going, but then I'll stop. When I got to 190 I thought, why stop here? Lets build some muscle and started seriously lifting weights while letting some more weight come off slowly. Point is, take it in bite sized chunks so as not to demotivate yourself.
And if you're like me, you dressed in unflattering baggy clothes. When you do get too small for them - treat yourself. Buy some clothes that you look better in. You'll be amazed at what that does for your self confidence.
Good luck, and if you have any questions or want some meal ideas send me an email. I'd be more than happy to share what I've found with you.