So the employment contract says that the company would grant you shares, and that these shares would be subject to vesting? But the company never actually issued those shares? So, when you left the company, the only paperwork you had about those shares was the employment agreement?

If so, it sounds like you don't own the shares, but the company owes you the shares. The fact of whether or not you own the shares should be easy to determine. The part that's harder (and requires analysis of what you signed) is whether or not the company paid you what you were owed during the period of your employment (including, if applicable, shares).