"However, we will never be able to build a completely human-like robot since robots will never be able to biologically reproduce."

You must not have seen the new Battlestar Galactica then...

This is a problem of understanding, not science:

The question "Will robots ever become just like humans?" implies that if robots were to become "just like humans" they would still be robots. They would not; they would be humans.

One might also ask "Will apes ever become just like humans?". No? What if they were smarter? What if they had human emotions?... What if they had a few years to evolve?

The original question is inherently flawed, which is why it may seem challenging. A less flawed question might be: "Will robots, or the (logical) descendants of robots ever have characteristics similar to those seen in humans, such as intelligent thought or a sense of emotion?".

With the fuzziness removed, the answer, barring premature eradication of the human race, seems obvious.

We are nowhere near making a robot which is like a human. What we're doing is making robots which LOOK more and more like one - and biological reproduction is not the big issue here. Even if we made a robot which looks absolutely indistinguishable from a human even at close range, which can replicate the movement of every muscle and joint, recreating perfect facial expressions... without the ability to THINK like a human they remain nothing more than Madam Tussaud's statues with some animatronics thrown in. We're getting close to making robots that look and act like humans, but we're light years away from anything that thinks and feels like one.

Not that there isn't a use for the robots we're developing. The primary advantage of a human-shaped robot is that it can occupy spaces and perform tasks using tools designed for humans. C3PO could sit in the driver's seat and drive you around much better than R2D2 could. However our C3POs still can't do much better than follow a set of programmed responses.

"Other than this, theoretically, robots could look, act, think, and feel like humans in every way. There are only technical problems that need to be overcome in achieving this."

This is a rather strong claim. If there are "only technical problems... to be overcome" then it follows that we must already know all the theory and rules behind human behaviour, thought and emotion. As far as I'm aware, we don't -- and we don't know how long it will take to work them out (if the problem is not intractable).

The technical problems facing roboticists and the AI community are no small matter but they pale into insignificance when placed beside questions on the nature of conciousness. The erroneous belief that AI is a "technical problem" seems to be making a lot of money for some pretty unimaginative technical researchers. Yes, Honda's ASIMO is a pretty impressive piece of kit, but a walking robot is no more intelligent than a wheeled one, and actually a lot less mobile.