The devil does his dreadful work of blinding the minds (νοήματα) of the unbelieving. We see with our minds. The spiritual battle rages in our minds. Satan is the god of this age who blinds unbelieving minds so they cannot see the light of Christ's glory in the gospel. And even if our gospel is veiled, it is veiled to those who are perishing, in whose case the god of this world has blinded the minds of the unbelieving so that they might not see the light of the gospel of the glory of Christ, who is the image of God (2 Cor. 4:3-4).
Paul knew well what it meant to be blinded so that he could not see the light of the gospel despite his exceptional education and brilliant mind. The expression, "so that they might not see," is somewhat difficult to interpret. It is an infinitive attached to a preposition (εἰς τὸ μὴ αὐγάσαι). The construction is ambiguous since it can indicate either purpose or result. The Hebrew way of thinking did not distinguish sharply between purpose or result/consequence (Moule, Idiom Book, p.142-143, see fn2). Satan's purpose is to incapacitate the mind in order to keep the mind from seeing spiritual truth and his purpose, because of his power, leads to the consequence that blinded minds don't see truth.
The verb translated "see" (αὐγάσαι) has two different meanings. This verse is the only place in the New Testament where the word is used. 1) The verb means to shine upon or illuminate an object as the sun shines upon the earth. The sense would be that Satan blinds the minds of unbelievers so that the light of the gospel does not shine upon them. 2) The verb means to see clearly or to gaze upon something or someone. In this case, Satan blinds the minds of unbelievers so that they cannot see the light of the gospel (Hughes, 2 Corinthians, p.129 fn35). The latter meaning is the better one in this context. The devil incapacitates the minds of unbelievers so that they cannot gaze intently upon the light (τὸν φωτισμὸν). This meaning fits with Paul's argument in the previous chapter about the veiling that hinders people from seeing the glory (2 Cor. 3:13).
A string of genitives follows the word light. It is the light of the gospel of the glory of Christ (τοῦ εὐαγγελίου τῆς δόξης τοῦ Χριστοῦ). When genitives are joined together like this, the first genitive governs the following genitive so the governing genitive would be the word "gospel" (τοῦ εὐαγγελίου). Gospel is likely a genitive of origin indicating that the light emanated from the gospel (Moulton, Howard, Turner, Grammar, 3:218). The next genitive, "glory" (τῆς δόξης) would describe the content of the gospel (Martin, 2 Corinthians, p.79). The final genitive, "of Christ" (τοῦ Χριστοῦ), would be possessive. Christ possesses the glory because He is the image (είκων) of God. The piling on of genitives emphasizes that Christ possesses the glory which is the content of the gospel from which the light emanates which can save our souls. We find here a summary of Paul's argument in chapter three.
The act of witnessing engages us in spiritual warfare. We cannot pull the blinders off from the minds of unbelievers no matter how brilliant our explanations or persuasive our arguments. The devil has incapacitated their minds, and only the persuasive power of God can remove the spiritual blinding. We wonder that unbelievers don't see the glory of Christ in the gospel as we see it, but the reality is that they cannot see it because they live in a world where the Son has been eclipsed by the devil! The shadows obscure the "Sonlight" until God rips away the veil of the devil on the mind of man.