Now that I am up and running on Ubuntu 13.04, I am going through all the functionality tests, in order to do what I did on my other set ups. I am on YouTube and I have no sound for the videos that I am attempting to play. My speakers are connected correctly and my sound is turned up. However no sound is coming out. Help! In order to facilitate this discussion and, I am sure learning experience, I will tell you that I am running a Intel Pentium 4 Processor 531 and I am housing an Intel Graphics Accelerator 900. I don't know if that will assist in any good responses, but that is all I can bring forth. I am not sure of the sound card. Thanks in advance for any input.

I've noticed lately that "YouTube" video are often started with the sound volume control (the one under the video, not your main one) set to zero, but not muted. Have you checked the position of the slider volume control for the video you're trying to hear?

I have, I have gone through everything I know and no sound. I made sure that the OS recognized my sound card, I went into the terminal and entered a play -l, noticed it listed, so this let me know that it was, in fact recognized

Have you tried using headphones? Have you looked at the device list(s) the the mixer for the sound system you're using?

You might find this thread useful. The posts in that thread by aus9 show how some sound issues can be investigated.