The problem is that you are trying to predict something where you don't have enough variables in your system.
You have a stock price that is without any context, so, did the stock go up or down because of a competitor? Perhaps there is a new competitor that stumbled, so the stock went up, but, should the competitor get their act together it could severely depress your company's stock.
If you company is a company that does outsourcing. If you don't take into account how the market rules can change then your prediction is going to be off, as, if companies have to pay extra taxes for outsourcing, then that will see a shift in resources.
Then you have weather and natural disaster events that can cause the stock to change drastically.
What you may want to do is to create a simulator, and the more variables you can include in your simulator the better off you are.
For example, what are the chances that an NFL strike can happen, as, you may find that you sell products to companies that sell to NFL teams, then that may impact your sales, so stock price.
You can model with a neural network, and it can come up with some way to accurately predict the past stock valuations, given a point in time, but it will not be any more accurate for future prices than a random walk would do, as it is a guess.
A simulator will give a range, given if certain conditions are met, then it's predictions may be closer, IMO.
UPDATE:
I don't believe a NN would be a good choice, since there is no way to test, after training, to see if the results are correct, unless you train up until June 2009, then pick values after that to see how well it did.
Using fuzzy logic may be your best bet, as it seems to deal with unknowns, but, you will probably want to get a range for the possible stock price.
If you are using web semantics, you may want to use some data mining, and see if you can determine what events may be the main predictor of a stock price change, then a neural network may be more useful.