At the beginning of Naruto's Konoha Crush Arc, Orochimaru grabs his former sensei, Sarutobi, and holds a kunai to his throat. However, instead of attempting to execute Sarutobi quickly, Orochimaru stabs his hand and lets him go. Letting one of the strongest ninjas, the 3rd Hokage go when Orochimaru attempts to destroy his village seems counterproductive and utterly illogical for such a calculating and cold individual. However, while Orochimaru's mind may be a chaotic mess, the motivations inside that mind can potentially be uncovered by looking into his past and overall disposition.
If the situation is taken at face value, then Orochimaru is bored by his admission. Orochimaru, being bored when he stands ready to murder his former sensei and wage war on the village he grew up in, seems unlikely. With all of his goals in sight: the destruction of Konoha and the forceful recruitment of Sasuke Uchiha, it would only make sense that Orochimaru would be anything but bored. He uses this admission of boredom and a feigned yawn to hide his real emotions.
The momentary tears that Orochimaru tried to play off could be from the sheer joy of what lies ahead or a small moment of mourning as he is about to try and murder Sarutobi. Letting Sarutobi go instead of swiftly dispatching him plays to his potential joy as he would rather face the Hokage, one on one, to prove his strength. But, on the other hand, with a glorious battle ahead and his goals on the horizon, Orochimaru could be experiencing an overwhelming and dark sense of joy and excitement.
There is also a chance Orochimaru had a rare warm-blooded human moment and felt remorse for what he was about to do. Sarutobi is the only father figure in Orochimaru's life. The time spent with Sarutobi, Jiraiya, and Tsunade affected Orochimaru to his core, as we see his sadness when Tsunade's brother dies. While his serpentine nature hints at a frigid soul, Orochimaru has a sliver of care for his motley found family.
Orochimaru's respect for Sarutobi as a ninja, sensei, and father causes him to hesitate rather than pull the trigger. Temporarily pausing and choosing to fight his sensei in direct combat would fit with Orochimaru's strange concept of family. Furthermore, loyalty between certain members of Orochimaru's band of misfits and himself hints at a manipulative but mutually beneficial type of family connection. Therefore, Orochimaru is capable of care and concern, even if they lack their traditional warmth.
Orochimaru prides himself on being among the brightest and most calculating ninjas rendering the deduction of his actual thought process tricky. However, Orochimaru's presence in the later parts of the series and sequel shows his humility and semi-compassionate nature. While he will always follow a scientific route that involves an emotionless and calculating worldview, he can be a human when circumstances arrive. Assuming Orochimaru's serpentine evolution chilled his heart isn't a stretch, but the deeper connections affect him in a human-like manner.
While stabbing himself out of boredom wouldn't be off the cuff for Orochimaru, reading deeper into his actions gives him a richer moral and emotional spectrum. Be it respect, fondness, or even hatred for Sarutobi, his impact on Orochimaru is profound and lasting.