You only have HDMI audio (from the Video card) and not PC audio. I do not see a sound hardware driver installed. I see one generic, basic function Windows installed High Definition Audio but that's all. The actual sound hardware driver is not installed.
First step is to install the correct sound driver, if there is one for Win 7. This looks like an older PC and it may not be (fully) Windows 7 compatible. If this is the case you will have to install a Win 7 compatible sound card. If the sound hardware was Win 7 compatible, Windows would have installed the High Definition Audio driver for the PC's sound and you would have sound.
A comment, not related to your sound problem. With this old hardware and only 2GB of RAM and a 64 bit OS, I'm surprised this does much more than load the Operating System.