There's one missing piece in the story here:
I told him if [returning the laptop again is] the best solution that he can provide (customer care is not an iterative process), I would have no option but to pursue this through my university's legal department.
So what was the best solution that the complainer wanted? It seems like a replacement would have been a pretty reasonable thing to ask for at this point.
This, on the other hand, from one of the complainant's Facebook replies: In that case, please give me all the details of Prawin K from Dells Bangalore office so that I can sue him in India and the US.
Pro tip from someone running a support team: threatening legal action is usually a surefire way to cause your support case to screech to a grinding halt, since this requires that lawyers get called in and support engineers have to stop work until they've done their due diligence. What's more, the result of that due diligence may be "we'd prefer not to have you as a customer anymore, kthxbai".
Then again, this buffoon on Dell's side clearly hasn't received that particular memo: He simply told me that Dell was a very big company and had ample resources to outlast me and my university in a legal battle. Facepalm.