No 25 SA - Has anybody ever received a top FT after no internship?

Brother, your career is a long way from over.  I totally understand where you are coming from.  When I was graduating, even coming from a top school, there were plenty of kids who failed to get the "prestigious" names on their resume that they had dreamed of obtaining since HS.  Most that I knew did everything right, but just didn't have the soft skills built up quite yet to get past the final round super day.  10 years out, most of these guys have caught up or surpassed many of the kids who did receive offers at top BB/EB/MBB.  I'm saying this as somebody who did receive an offer at a top bank right out and have stayed in contact with many of the guys I graduated with.  The ones who ended up successful shared one common ability: the ability to prevail.  You may be too young to understand this now, but what job you have first year out of college is really only 1% of what it takes to attain long term success.  Many of the people I saw took an alternative route, whether that's taking an offer at a boutique/big 4/corporate position and then hopping into a top MBA program, or going straight into a top MsF program and then re-recruited for Summer Analyst positions post Sr year.  My trajectory was BB IB-->MBB-->T1 RX CO, and throughout my career, the one thing that keeps surprising me is how disillusioned the odyssey for prestige, money, and corporate glory can really be.  Being surrounded by people who care about those 3 items more than waking up the next morning really skews the meaning of life and the meaning of having a job in general.  These people are often so caught up in the mindset that a prestigious job will bring this ultimate sense of self-fulfillment and fix every ailment or insecurity they've ever experienced that they lose sight of the true meaning of life (starting a family, maintaining real friendships, taking care of their loved ones, doing work they are truly passionate about, giving back to their community and neighbors, making the world a better place to live in, etc).  Please don't delve your emotions so deep into this distorted disposition that you feel you are worth less as a human being just because you didn't win a competitive internship. 

 I know you wanted to hear direct and actionable advice on what to do to combat your undistinguished resume for FT positions but, first, you need to know that what you are feeling right now is normal, but that doesn't mean it's the right way to go about life, but what you should be doing is 

#1. Very bluntly, stop feeling sorry for yourself.  Take the words "unlucky" and "lucky" out of your vocabulary.  If you keep thinking that the results at the end of a super day boil down to luck, then you will 95% of the time find yourself on the other end of the spectrum.  By feeling that success is about "luck" you are putting yourself into the disposition that there is nothing more you can be doing other than allowing the world to spin while you wait for it to hand you your slice of the pie.  Start reflecting on what you could have done better.  Were there any moments of awkward silence in any of the rounds?  Were there any technical questions you weren't prepared for?  Did you go out of your way to introduce yourself to people in the office?  Did you keep referring to the paycheck or prestige when asked "why insert firm name"? Did you follow up with thank you emails? Did you take the time before the superday to learn recent firm initiatives/deals and build real relationships with any of the guys working there?  Did you do a good enough job at convincing the team that you are passionate about the work and a hard enough worker to learn the difficult technical skills?  If there was a superday dinner or lunch, did you sit around and wait for people to ask you about yourself or did you come prepared to conversate and make yourself out to be someone they can sit in a room/airport with for hours at a time? Are your excel skills up to par with your class mates receiving top offers?

#2. Look for ways you can leverage your unpaid work experience into something that will pay you well enough.  Look at people who worked/interned there prior to you.  Where did they exit to?  That is a connection just as solid as a school alum.  Take this internship as an opportunity to gain experience in different areas.  Ask for more work, even if you feel you are being robbed because of lack of compensation.  

#3.  Look for firms you would love to get full time offers with, and target the ones that have brought kids on that weren't traditional Summer Analysts/interns prior to Full Time.  Begin reaching out to people now.  Get any application like rocket reach or Apollo that allows you to find email addresses with just a name.  Reach out to as many as possible until your fingers are sore.  Places that recruit for FT certainly exist, and even if you have to go to a Big 4 or smaller Accounting firm, this "brand name" will definitely allow you to penetrate more prestigious firms later on, given that you can either network and show tremendous technical aptitude or rotate in from a Top 15 MBA program.

#4.  If #3 doesn't pan out, look for top MsF programs (Vanderbilt, UVA, UT, SMU, UCLA, Indiana U, Georgetown, Villanova, Johns Hopkins, MIT, Princeton, the latter of which are quant) and then look to re recruit for SA or FT positions, and this will expand your alumni network tremendously.  

I get that it feels like your life is over, but if you can show some grit, and continue to improve yourself professionally and personally, I can promise that you will find yourself exactly where you want to be in 5-10 years laughing at yourself for being so ignorant and feeling your career was over at 21 years old.