[ImperialCrown]

1984-1995 AS would be the minivan generation before the 1996-2000 NS minivan and the cowl drain system would be different. Your drains are off to the left and right ends of the cowl plenum chamber, into the front fenders and drain out onto the ground behind each wheel opening.
You need to locate the water entry point. The HVAC does have the fresh air intake in the cowl plenum and if the water can't drain from this area, it will enter down into the HVAC housing and leak onto the right front carpet.
With the wiper screen removed, run water into the plenum area with a garden hose under low pressure. Watch for a plugged drain in the cowl or have a helper inside the van watching for water dripping. Many times a cowl full of water will leak onto the floor after a sharp turn after an overnight rainstorm, for instance.
You also want to be sure that the A/C evaporator drain coming out of the right side firewall is clear of debris. This offers another escape for water build-up.
The rubber antenna grommet where the cable enters the body behind the right kick panel is also a common water leak point if the grommet got dislodged from its sheetmetal opening.
You may want to remove the carpet for washing and drying to avoid moldy odors. The jute backing may have to be discarded as once this material starts to stink, there is little remedy for it.

 

[ImperialCrown]

You may want a good service manual if you are going to service the vehicle further. It just makes it easier to read a repair procedure order of disassembly or to see a picture on how something comes apart.
A main public library may have more detailed (or even factory) service manuals to take out on loan or to photocopy. Some large city libraries might have an internet subscription to Alldata.
Where the HVAC housing meets the cowl plenum there should be a foam gasket to prevent air leaks and a raised sheetmetal lip on the plenum side to keep water out. There is a black plastic shield covering the actual HVAC air intake.
Tree debris is the worst offender for plugging up water drains in cowl plenums and sunroofs.
You would only have to pull the front wheel inner fender splash shields only if you didn't see water draining onto the ground.
The antenna cable grommet is visible, but tight to get at from inside the vehicle. You don't have to remove the A/C housing to access it. If the cable grommet has dislodged from its hole, it may be easier to get your hands on it to reseat it if you have the right inner fender shield pulled away. Dried water leak trails may appear as whitish drip streaks from the source of the leak.
Pulling out the carpet will require the removal of the seats and floor trim pieces. It is a one-piece carpet AFAIK. Again a good service manual used as a guide will help here.