I don't know about going straight to a work at home situation but I could choose to do my job from home. With my job, first, you have to go through the usual training and succeed in an office setting. Then you can become a teleworker. I have heard that if you are handicapped, you can request it as "reasonable accommodation" even if they aren't advertising teleworker openings. So that might be one means to get a real stay at home job with a reputable company: Do a little research on local companies that allow telework and find out what the process is to become a telworker for them.
Good luck with this.