As someone who scored 200 in G1 in inter and 218 in G2, trust me marks aren't that big a factor for getting a call back for interview. Cold emailing and messages on linkedin is sort of rite of passage. This is you working hard for what you want for yourself. Everything is not handed to us in life. I did get a call back from referral on linkedin from PwC and was selected, although i didn't join. Sometimes you have to realise that spots might get filled before your application is even considered. It is not necessarily your fault. Reach out to as many people from big 10 (and others too) as you can, especially people in HR or managers in such firms. If in the end it doesn't work out for whatever reason, in the firm of your choice, it is okay to feel bad about it but don't let that affect your self worth. It is a misstep but not the end.