Why does the Bible ask people to repent and believe if they are unable to respond?


That's an important question... As R. C. Sproul once said, "God is not going to negotiate His holiness to accomodate us".  As fallen creatures God does not lower the bar of his holiness  He still requires of us to obey his comands perfectly, even though we are morally incapable to do so. Our inability does not alleviate responsibility, including our responsibility to obey the command to believe. Fact is, fallen men are unable because they are unwilling. By nature they are hostile to Christ.

Perhaps think of it like a farmer planting crops. He casts seed after plowing up the fallow ground, but nothing will happen to the seed unless the blessing of rain come down from above. The seed is not sufficient to produce life by itself without the proper conditions. Likewise, we cast the seed of the gospel into the hearts of men, but unless the Holy Spirit plows up the fallow ground of their hearts and "germinate" the seed of the gospel, no fruit will come forth. We call men to repent and believe, but their hearts are willful and hard. Only the Holy Spirit can disarm the hostility and quicken them to life (John 6:63, 65). We plant and water but God causes the growth. (1 Cor 3:6) Only as the Spirit gives us a new heart do we see the truth, beauty and excellency of Christ in the gospel.

God calls all men everywhere to repent and believe the gospel but they reject the message...but to those who are inwardly called through the message, salvation.

Paul said,

"we preach Christ crucified, a stumbling block to Jews and folly to Gentiles, but to those who are called, both Jews and Greeks, Christ the power of God and the wisdom of God." -1 Cor 1:23-24