Your computer may not be able to handle sound coming from multiple things. I've found that if you have multiple things open that use sound card memory, it can't handle it and selectively chooses not to play sounds from one ore more of the most recently opened programs. Particularly if you have a voice chat program open such as Skype (which tends to hog computer resources and lag if anything else even slightly large is open) and are in a call while trying to test-play RPG Maker, it simply won't have sounds working for your game. This could be seen as a good thing cause if you don't have headphones and have an internal mic or stand mic you might have sounds coming from your computer going into the mic. But in this case you want your sounds to work. So IF you have other programs open that draw heavily on your sound card, just close out anything not needed and only have RPGmaker open.
Also remember that based on the ghz your computer can handle, it might simply not be able to process all the information needed to play the sounds, but this, again, would also be based around how much you have running. Just close non-essential programs and try again.