Question edited for a lot more clarity.
Question moved from 'Power Computers' to a better category.
The manual is dreadfully vague
Note: The Console (4) can be operated with an optional power supply instead of batteries. To purchase a power supply, call the toll-free telephone number on the front cover of this manual.
Plug one end of the power supply into the jack at the front of the exercise cycle. Plug the other end of the power supply into an appropriate outlet that is properly installed in accordance with all local codes and ordinances.
Look on both sides of the console and also at the front of the bike itself. I have to say though, if the console didn't work with batteries, it is unlikely to work with a power supply. It is broken and that is why it didn't work with batteries.
What you could do is follow the wiring harness as shown in the parts manual from the console down and where it branches off to..
Aha, I found this
Exercise Equipment Technician:
treadmilltech
It should plug in at the bottom of the front where the 2 side shields come together or it will go into the console itself in the back.
https://www.sportsmith.net/images/product_support%5CNordicTrack%5C216731%20-%20NORDICTRACK%20AUDIORIDER%20R400%20EXERCISE%20BIKE%5CNTEX4196.1-247436.pdf
https://www.google.com/search?q=nordictrack+audiorider+r400+mains+adapter+operation
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