"If my computer gets an average of 250Mhash/s, what is the maximum amount of time it would take me to solve a block, and get 50 bitcoins?"
An infinite amount of time. Since your 250Mhash/s currently accounts for 1/44124th of the network, you have a 1:44124 odds of solving any particular block. However, your odds do not automatically get better with time.
To give an example of this, if you were playing a lottery that had one-in-a-million odds and you played the lottery a million times, you are not guaranteed to win even once. On the other hand, you might win twice or even more. It just depends upon luck.
If you're interested in the really complicated math you can figure out exactly your odds of solving a block on any particular day, week or month - but with your hash rate I'd suggest that if the difficulty were to stay the same (which it won't) you'd solve a block every 10 months on average.
You'd be much better off to mine with a pool, and get smaller, more regular payouts. I recommend Triple Mining as one of the best smaller pools out there; the link is in my sig.
I did not know that. So if I understand you correctly, although every block has a solution, it is theoretically possible (Although insanely unlikely) that a solution will never be found?
Or does this mean that I can never be given my "Own" block to solve, and there will always be others working on it even if I am solo mining, thus it is guaranteed that the block will eventually be solved, but whoever solves the block gets all the bitcoins?
Now that we have broken the ground on how this works a bit, is there a place I can go and read a bit about this more technically, but written for the average joe to understand. Basically I am not looking for the information on where a block comes from, and exactly how you go about solving it so that I could in theory, if I had nothing better to do with my time solve a block by hand. (Yes, I understand this is absurd, but if I know enough how to do it on paper, despite the fact it may take me the rest of my life to do but a single hash, or not, I will understand exactly how it works.) Its more for curiosity.