I found that the AC does not seem to work.
There is a diagnostic procedure in the repair manual which says
Simultaneously press Off and Foot (air flow) switch and then within 2 seconds Auto switch
Self Diagnostics will start and some codes will be displayed if faulty.

In my case nothing happens when I try this.
The air flows but no cold air comes out.
The repair manual says replace the control unit in this case.

Is the control unit a frequent point of failure? I had seen a video in which a guy replaced it by getting a used one from Ebay.

It isn't frequent for Nissan HVAC heads to fail, but cracked solder, corroded circuit boards, or components dead from old age can certainly happen on a 26 year old car. With Front Air Controls that are part of the console panel like the one on your Quest, when the lights are on but they won't go into diag mode, it usually means something wrong internally.

did you rule out low refrigerant and the AC clutch is powering on?