Even though there is already an accepted answer to this question (which I don't agree with), I would like to point out the fact, that scientifically speaking, already the term "Hinduism" is much more complex than "Christianity" or "Islam", which of course also renders the dating business much more difficult.
While some people identify the two, scientists of religion generally differentiate between the Vedic religion of sacrifice and "classical Hinduism". So depending on what you are talking about, also the answer varies. If we identify the two, then @Vineet Menon is perfectly right to let the history of Hinduism start with the oldest parts of the Rigveda (not earlier than 1500 BC).
If we don't, then we can let "classical Hinduism" start for example with the rise of the 6 orthodox systems of philosophy, in all probability essentially as a reaction to the philosophical and numerical winning of ground of Buddhism. We can date this somewhere between 200 BCE and 200 CE (here we can expand the discussion limitlessly). Even in this case, the Vedic Religion, though not identical with Hinduism, remains its ancestor.
Conclusion: it is very much a question of how we define "Hinduism". Since we don't have a single (historical) founder of the religion and no clear cut starting date, this is open to debate (and personal liking). To give an example: Some (many?) Hindus regard Buddha as an avatar of Vishnu and therefore Buddhists as Hindus. Most (all?) Buddhists would disagree. Same holds true, to a lesser extent, with Jesus.