Success!

I followed Ernie's advice and found the door manufacturer's name on the inside of the hinge (Therma-Tru). I did some Googling and found the company and emailed them my plight.

I got a response right away and the representative sent me not one, but three(!) new hinge pins, for FREE! I just got them today and pounded the missing one in and it fits like a, well, a hinge pin. Excellent!

Thank you everyone for all your helpful advice. I spun my wheels over this for a loooong time and now that it's resolved, I can move onto other household projects! Yay!