Having taken Batavia, Sultan Agung would immediately move to his archenemy, the sultanate of Banten, and conquer it. This effectively unites Islamic Java. His next goal would be Blambangan (which he did conquer OTL in the mid-1630s), the last Hindu part of the island.
By 1635 all Java is united under Mataram.
But all this isn't very far from OTL. Mataram really failed because of Sultan Agung's son and heir, Amangkurat I. Amangkurat is widely considered by the Javanese to be the epitome of a tyrant, and for good reason:
- He murdered basically all his father's ministers and replaced them with sycophants, causing the Dutch to remark on "this strange manner of government in which the old are killed to make place for the young."
- He executed 2,000 Muslim clerics and their wives and children. Their bodies were left rotting for months afterward, a serious offense to Muslim funeral rules.
- He banned all ships, even fishing boats. Note that Java is, you know, an island. All private trade was also banned.
- His arrogance ruined any hope of Mataram participating in a wide anti-Dutch alliance, while Mataram's overseas vassals saw no point to swearing fealty and gradually just stopped sending tribute.
- By the 1660s he was refusing to let his dead wife be buried, spending months besides her rotting body. As you can see, by this time he was, well, totally insane.
This wouldn't change even if Mataram kicked out the Dutch.
The real divergence would start in the 1670s. In the 1670s, Trunajaya, a prince from Madura (the big island right next to northeast Java), revolted, totally crushed Amangkurat's tottering regime, and very nearly founded a new dynasty until the Dutch and their Sulawesi allies came in. Without the Dutch, Trunajaya definitely wins.
Now, the demands Trunajaya made during his rebellion were twofold. First, a Javanese king should not have anything to do with Christians like the Dutch because the Javanese are a Muslim people. Second, a true Javanese king should have his capital at Majapahit, the capital of the greatest empire in Javanese history. If Trunajaya became king, he would surely have moved his capital to Majapahit and founded a new and strongly anti-European sultanate there. And considering Majaoahit's proximity to the coast and Madura's coastal maritime traditions, this new Majapahit could become a vast maritime empire just like the original Hindu Majapahit.
Oh, and another divergence to think about; if Mataram conquers Banten, the English will have to buy most of their black pepper somewhere else--most likely Aceh. This could strengthen Aceh and help it not decline into feudalism as it historically did.
ETA: And a Dutch East Indies would still exist without Java, it would simply focus more on Maluku (perhaps with Melaka as a more central holding when it's eventually taken).