Lawyers of the OT, how do I collect on an unpaid invoice?

My very small business sold a part to a very large, national, well-known chemical company for use in their local plant. The invoice is close to $15,000.00. Terms were 30 days. They are now over 100 days late paying the invoice.

I've been getting the run-around from their "accounts payable" team which is clearly located in India or some other foreign country based on the cryptic email replies I receive. Local people can't help because they are "not accounts payable."

Apparently, the accounts payable department paid Fed Ex of all people instead of us. They keep saying they "paid the invoice" and show us the cancelled check which shows it was made out to Fed Ex and deposited by them. In the meantime, we have not been paid.

When we explain this in an email [multiple, multiple times], they reply weeks later with another dumb question like, can you send us a copy of the invoice [already done a million times] or can you "double check your records to make sure you haven't been paid?" or other nonsense. Then we wait weeks again for a reply.

After 30 years in business, this is really the first time we haven't been paid, so we don't know what to do. If I hire an attorney, does the chemical company have to pay his fees once they are ordered to pay the invoice [which will happen -- this is very clear-cut]? Can I file something myself in a local court? I really don't know where to begin as there isn't much profit built into this particular transaction and I'm trying to keep the overhead in solving the issue low.