It sounds like we are definitely dealing with a driver issue here if the sound worked fine before the reformat/reinstall.
The first thing you might try is to go to Dell's site and download the latest driver for your laptop's sound card and install it. Here is the link to Dell's driver site where you can enter your Service Tag # and it will show you a list of the drivers for your laptop.
Dell Driver Downloads Find the Audio Driver and download it to your pc and then install it by clicking it and following the simple steps. It might take a restart for the changes to take effect.
Try this and let us know if it works. If not, we'll go from there.
Good luck.
- Jason