First of all, I am not an expert.
But, after reading hundreds of topics here and there, I can tell you that you still have a good chance,
but if I were you, I would apply to schools ranking between 30 & 80. Without publications / research experience, and with unrelated work experience, you cannot hope at any top 20 university, especially that you are not planning to take the PGRE.
Again, that is only my opinion, based on a lot of reading, but others may suggest other options.