It depends on whether Wal-Mart was negligent in thinking that you stole the laptop. Wal-Mart is going to say, "just because he wasn't convicted doesn't mean he didn't do it." I.e., Wal-Mart won't say "we got it wrong." Wal-Mart will say "the jury got it wrong."
Don't gamble your freedom on a public defender. "Public defender offices and other indigent defense providers are underfunded and understaffed. Too often, when legal representation is available to the poor, it’s rendered less effective by insufficient resources, overwhelming caseloads and inadequate oversight." - United States Attorney General Eric Holder, 2013