From this website, I figured out it was probably either a spring or a spring link that broke. Since I didn't want to pull out the dishwasher more than once, and could not tell which side was broken, I was glad I ordered two spring links AND two springs. Turns out the right side spring link was broken and when it snapped, the spring went flying somewhere out of sight. Went ahead and replaced both sides since the dishwasher is about 20 years old, so if one side was weak enough to break, the other would soon follow.
The only issue I ran into that was not addressed in the video was that the new counter top was installed long after the dishwasher was installed, so had to adjust the leveling legs in order to clear the counter top when trying to pull the dishwasher out of the cabinet. Once that was done, the video pretty much covered what I needed to know. Thanks!