How Old is Hamlet?

When I read this play before, I always envisioned Hamlet as a young man, probably about my age. Some scholars might believe this is because "Hamlet represents every man," or something completely broad and generic like that. Hamlet's emotions seem to be a bit more irrational than someone of an older age, as he's portrayed in the movies that I've watched, so it's a bit perturbing to see forty-year-old Mel Gibson playing the young prince that I imagine in my mind. As well, the play places young Hamlet as a student in college, away from the kingdom. As well, if he were so old, why would he not assume the throne after the death of his father, rather than his uncle? Things are not really adding up. In the play, there are lines that say that Hamlet is about thirty years old. When delivering his speech about Yorick, he talks of him being dead for about twenty three years, which would mean that Hamlet was about seven when he died. That makes sense, but it doesn't seem to fit with his personality. I would hope that a thirty year old man would be less prone to madness, even despite all that has happened around him.