This is a typical case of an incomplete reinstall. Frankly speaking, we often see that here.

If you use the Dell provided system restore media (of partition) to reinstall the original OS, you'll have sound. So it seems you didn't. Why you didn't is unclear.

If you use any other version of the OS or even another OS, it's your responsibility to install all drivers. With your service tag, you should be able to find them on