I have been there and done that. Sent LinkedIn messages but never got any response. I understand where you are coming from. I do.
Then I reflected on that and thought about the many times I rarely responded to any LinkedIn messages sent by someone who I have not met or had no common connection what-so-ever. I realized everyone is busy and also may not want to spend any time or energy on someone who they have no connection - or want to protect themselves from potential spammers.
What is in it for them? - That's the hard truth that rarely anyone wants to spend any time or energy on someone who they have connection. It doesn't matter if you are from the same school, city or an entrepreneur like them.