Well you could say it's both and neither - under extreme pressure a gas takes on the properties of a solid - therefore at the centre of the sun it is likely to be solid to a degree - of course at this depth it's also the centre of nuclear fusion and fission and immense heat. It's more a plasma than a solid though. For a detailed explanation of the sun's structure go here: http://en.wikipedia.org/wiki/The_sun#Structure

Neither, the sun is a ball of gas, but it is not burning, it is undergoing a fusion reaction.

Think of it more as a huge hydrogen bomb going off constantly.

It is a big ball of gas, with nuclear reactions occurring at the centre, and there is about four billion years left in the tank - about as long as the sun has existed so far.

Actually, we really do not know the exact age of the sun, but it has 5 billion years to go before it swells up to be a red giant. When I first read that it has only 5 billion years left to live, I thought it meant that the sun would cease to exist permanently. This was the time I was about eight or nine years old.

You actually are partially right. The Core is 150 times denser than water so it could well act like a liquid (or even solid) under such immense pressure, this is surrounded by a hot gas convection zone that ferries heat to and from the core to the surface. The surface is hot ionized gas (plasma a fourth state of matter) that you can see acting under the influence of magnetic fields where you get projecting loops from the surface. I should state that since we can't see inside past the photosphere the inside is all guesses based on science so just like we can't say for certain that the interior of the earth is actually like it is, the same still goes for the Sun. But since that's the structure that would occur in order for the Sun to remain as a Sun in our current understanding of Science that's how the interior is believed to be. The Sun has been alive for 4.5 billion years (very roughly) and is considered middle aged, this means there is another 4.5 billion years left on the clock. If there was only 10 million years left on the suns life I would get worried as it that's not a long time in the whole age of the Universe and once it's gone it will start to leave the Main Sequence and evolve into a Reg Giant, which will kill off life on this planet. As it gets near the end of its life the Sun will actually start to get slightly hotter (as the core starts to run out of hydrogen and so the layers that radiation pressure used to support start to collapse inwards heating the core).

sorta both

Guesswork, we won't be around!