For your benefit:
a) Asking for partial payment sends a bunch of signals regarding your level of professionalism and need to see this check. Those signals are not helpful in getting you paid in a timely fashion.
b) Two weeks late is practically on time for a lot of clients. Many are just structurally incapable of getting checks cut that fast. Yes, insane, but also true.
c) I'm uncertain of the status of the project and your ongoing relationship with the client. Please note that escalating to lawyers is not in general something which improves client relations, if you wish to get more work from them in the future or if you have an ongoing work relationship for e.g. future milestones.
d) Prior to escalating to a lawyer, write them a short letter yourself and FedEx or courier it to their office. Pay the extra for signature confirmation of receipt. Contents could be similar to:
Dear $DECISIONMAKER:
I invoiced you ($IDENTIFYING_INFORMATION) for $AMOUNT on $PROJECT on $DATE, but to date have not been paid. Last week I spoke to $NAME and $NAME, who promised to handle this issue, but it remains unresolved.
The invoice is due immediately. I would prefer that we resolve this amicably without having to bring lawyers into it. If you have any questions, please call me at $CONTACT_INFO.
Regards,
$YOU