Is it possible for absolutely everyone to attain enlightenment? As seen in the title of this question, I'm not sure whether everyone is able to attain enlightenment.

As far as my study and introspective analysis have shown to me, it seems that in order to uproot ignorance permanently, one has to be able to correct the distortions of the mind (perceptions, thoughts and views). And the only way to do that effectively is through right understanding about reality (dukkha, the illusion of the self, impermanence, and the Dhamma in general).

But what happens when one is factually limited to exert that right understanding? 
What happens when one cannot exert self-control, or when one is handicapped to use logic, language, cognition or the capacity for thinking abstract thoughts properly? 
(I'm really sorry if I'm using some words in a rude fashion; english is not my first language)
I'm talking about biological or physical limitations that may impede a normal use of mental abilities (lack of cerebral structures, disease or anatomical abnormalities, lack of development of faculties, etc.).

What do the suttas tell us about this?
What is your personal experience in with this topic?
What does scientific research tell us about this?

I'd appreciate any kind of answer.

Thanks in advance for your time and patience.
The nature of mind is clear light,
defilements are only adventitious.

-- Dharmakirti

In my view, enlightenment is possible -- if not within this lifetime, then in other lifetimes. 

From the point of view of the doctrine of Buddha Nature, all sentient beings possess the inherent seed for enlightenment. The Dalai Lama says: 


  Every sentient being—even insects—have Buddha nature. The seed of Buddha means consciousness, the cognitive power—the seed of enlightenment. That’s from Buddha’s viewpoint. All these destructive things can be removed from the mind, so therefore there’s no reason to believe some sentient being cannot become Buddha. So every sentient being has that seed.


Logically, karma must have fruition, and the mindstream follows the path of Samsara endlessly until it reaches Nirvana. Otherwise, it will always reincarnate, experiencing karma in the process. All karma is impermanent, as Buddhism suggests. From these premises, any karma -- negative or positive -- must come to an end. Even individuals having committed much negative karma, as Milarepa or Angulimala, reached high levels of spiritual capacity.

As to your question more specifically, for individuals cognitively impaired, such individuals may develop merit within their lifetimes, which will help them in future lives, even if they don't follow the path in its entirety. 

To perceive this lifetime and the next as fully separate is against the idea of dependent origination, entailing linkage between cause and consequence. From the view of emptiness, the division of this life and the next -- as well as many other such divisions -- is empty of intrinsic nature: it exists on the basis of appearance alone. Merit, from this point of view, is indistinct from the realization of the spiritual path; the Buddha committed many compassionate acts in previous lives which furthered his enlightenment. 

Therefore, from the view of the two truths of Nagarjuna, merit is karmically linked with enlightenment, on the basis of conventional reality's cause and effect. In other words, merit furthers enlightenment, and can be developed by individuals incapable of deeper cognition. 

From the point of view of ultimate reality, in the same framework, I recall visiting a Buddhist temple where a Tibetan master explained how emptiness entails a division into parts. Even if a person cannot fulfill enlightenment in this lifetime, they can contribute to it in by right deeds, and even with very partial deeds. If compassion meditation consists in various altruistic intentions towards others, then why not a few intentions? Even one intention? Anything a person is capable of may fulfill a virtuous purpose. 

For someone unable to commit any action on the basis of great disease or such things, then their life may consist in experiencing negative karma accumulated previously. In diminishing this karma they also promote later enlightenment. 

In sum, I suggest enlightenment should be perceived in the context of multiple lifetimes. Otherwise, many individuals might conclude it is not possible for them, and commit detrimental acts. They would be forgetting the wholeness which the Buddhist path possesses. 

P.S.: Isn't it that even for people deficient in a cognitive sense, that their minds still possess the capacity for virtuous and detrimental acts? Any mind entails various possibilities, leading either towards or away from enlightenment. And if a person failed to have the capacity of choice, i.e. the capacity for intention, then I'm unsure how this lack of intention would arise karmically speaking. In any case, I wish this helps!