I'm a one man show developing a C++ Windows application for a customer. Over the past several months we've been running to the same problems with missing DLL dependencies on customer machines. Despite my best efforts something keeps going wrong and we get angry emails back. My boss and my boss's boss are angry with me and the customers aren't happy.

I'm hoping you guys can help out and give suggestions/ideas on how to get the deliverables in order. Before some of the obvious:

1. I have no test machine. That is, I can't replicate the customer environment nor attempt to install the app on a "clean" system to catch gotchas before shipping.
2. I've tried using depends.exe to track down what versions of the DLLs my project is dependent upon. I'm shipping our code with the redistributables I've been able to find that way. After that it's an angry customer email waiting game.
3. I'm required to use a third-party DLL which can not be registered (it's buggy as hell.)
4. I'm not supposed to use Install Shield, any other automated installer, or write an install script.
5. I provide written instructions on how to get the app installed (unzip, double click exe file.)

I'm tired of taking heat for this stuff. What am I missing that I could be doing? What should I ask in terms of support from my employer? How should I ask for that support in a way that they'll provide it?