<p>Wow, you certainly have had an uphill struggle. Sorry to hear about your problems 
This website has a list of test-optional schools, where you will have a better shot, but the bad news is that only one of them is an engineering school:
[SAT/ACT</a> Optional 4-Year Universities | FairTest](<a href=“http://www.fairtest.org/university/optional]SAT/ACT”>ACT/SAT Optional List - Fairtest)</p>
<p>Also of use - a list of schools that meet 100% of student’s need for FA:
[Colleges</a> That Claim to Meet Full Financial Need - US News and World Report](<a href=“http://www.usnews.com/education/best-colleges/paying-for-college/articles/2012/02/16/colleges-that-claim-to-meet-full-financial-need]Colleges”>http://www.usnews.com/education/best-colleges/paying-for-college/articles/2012/02/16/colleges-that-claim-to-meet-full-financial-need)
Any schools that are on both of those lists deserve special consideration!</p>
<p>The one engineering school that is test-optional is WPI. Also, they would appreciate your participation in FIRST robotics as they are a major supporter of that program. They even have special scholarships set aside for FIRST participants -
[Undergraduate</a> Admissions: WPI FIRST Scholarships - WPI](<a href=“http://www.wpi.edu/admissions/undergraduate/apply/firstscholarships.html]Undergraduate”>http://www.wpi.edu/admissions/undergraduate/apply/firstscholarships.html)
WPI was the first school to offer an undergrad degree in Robotics Engineering, and now has MS and PhD degrees in that field as well.
I think it might be worth applying. The obvious downside is that WPI is far from home, and they do not guarantee to meet 100% need for FA. But you never know…
Another point - you said you used your application to explain your circumstances. Did your guidance counselor also explain your circumstances in his/her recommendation letter? If so, that would help bolster your case considerably…That is what they are supposed to do, help the college fairly evaluate your application by providing some context.</p>