HI there! Thanks for reaching out! Here are a few thoughts.
First, being homeless & ill are definitely enough to explain a low GPA, although they may wonder why you didn't just take some time off from school given those tough circumstances. But that said, it sounds like you have strong reasons to explain what happened with your grades & you could easily use the optional essay to do that. Harvard Extension school is fine - it's not nearly as hard to get into as Harvard or an Ivy League so it's not going to carry a lot of prestige unfortunately but it is fine.
It's a bit hard to give you a sense of your chances without more detail about your work experience & specifically the impact you've had/accomplishments. You will need to be much more specific about your goals as well. There are a million different ways to make the world a better place, so how exactly do YOU envision doing that? Saying you want to start your own company is actually a fairly tough goal when it comes to b-school apps. When it comes to entrepreneurship what matters is how convincing your argument is for what exactly you plan to do, why you want to do it and HOW you will be different and better than everything else out there as it relates to the problem you are trying to solve. Given the need to explain how you will be better (and how you can do it better even with more limited resources than a large firm) is the reason why saying you want to be an entrepreneur is also one of the toughest goals. It's often easy for the adcom to poke holes in your argument & you can expect that they will be grilling you in an interview to see how well thought out your goals are! That said, if you do have a strong clear idea for the type of business you want to start & the unmet need you plan to fill/problem you plan to solve that is definitely a way to differentiate yourself!
One other issue will be your age & years of work experience. You will be quite a bit above the average for top schools & that makes it tougher to make a "why MBA" argument. Schools worry that you are too experienced and no longer need the degree. There are definitely ways around that but that is one thing to keep in mind as you work on your apps. You may want to consider EMBAs, where age will not be a factor & you will be right in their range. There are a lot of benefits to an EMBA, they are easier to get into, and you get access to the same great professors & alumni networks.
Hope that helps & definitely reach out to us if you are curious to hear more about what it's like to work with
Admissionado & to talk in more detail about your candidacy. Just reach out to Claudia at
claudia@admissionado.com and she can set you up with a free consultation!