The left most light key constantly glowing would definitely be a case of two pins being bent, and shorting out.
Try troubleshooting your issue, removing the light key module. If it solves your scrolling problem, then you have found your culprit.
Super carefully remove the cable, both in the Arduino keyboard end, and the light key module, and inspect the pins. It is most likely one of the end ones, relating to the left light key.
The pins are so small, that they can end up both going into a single jumper end of the cable. You may need to straighten the pin out. Definitely remove it from the plastic shell before doing this.
Likewise, it might be an idea to insert the cables while it’s removed, removing any additional margins of error.