The HVAC Box is in the front of the car and is mainly used to route the air flow from between AC and Heat.
The Resistor Pack is used to control the speed of the fan that distributes air into the cabin.
The AC Condenser is in front of the car and cools the air going into the HVAC box utilizing the AC Compressor in the back to pressurized the coolant.
Slow Answers: The AC system in the Elise is very similar to all cars but because of the mid engine layout involves more logistic issues than in a front drive car. Everything is either hidden, in a tight spot, or buried in body work and trouble shooting is a real pain. When you stated that the pipes show no leak I believe that you are referring to the rubber pipes from the AC compressor to the bulkhead connections in the back right side of the car. The rubber pipes are connected by the bulkhead fitting to long solid pipes running down the sill on the passenger side to the front of the car. If these are leaking, hopefully not, they cannot be directly replaced with out tearing out the sill. BUT
, they be replaced with proper rubber hoses. It is still a pain but doable, believe me I know. Did that, done that.
Working on that AC system is not for the faint of heart. It requires some specialized tools and a good knowledge of how it works. Even then, many AC shops won't touch the Elise for the aforementioned reasons. My first recommendation is to find out what is actually wrong by answering a couple of basic questions:
Is the system holding the AC charge or is it leaking? If it is leaking, then where?
If the system holds a charge, does the compressor kick on when the AC button is engaged?
If the compressor kicks in and the high and low side are within specs, is the front HVAC flapper valve moving to direct the air properly?
There are many hints, fixes, helps and ideas throughout this forum that deals with AC issues. Suggest that you search them out. You can PM me if I can help.