“could not believe” does not mean that they had their eyes blinded or their hearts hardened against their wills. They chose to do evil. It was a deliberate choice on their part to reject Jesus and His message and as a result of their choice, God gave them over to what they really wanted (Romans 1:24, 26, 28). Plummer notes that “Grace may be refused so persistently as to destroy the power of accepting it. ‘I will not’ leads to ‘I cannot’”. Murray observes “We must never forget that it is by God’s appointment that if His word does not quicken, it must deaden.”

Romans 1:24  Therefore God gave them over in the sinful desires of their hearts to sexual impurity for the degrading of their bodies with one another.

Romans 1:26  Because of this, God gave them over to shameful lusts. Even their women exchanged natural relations for unnatural ones.

Romans 1:28  Furthermore, since they did not think it worth while to retain the knowledge of God, he gave them over to a depraved mind, to do what ought not to be done.