. . . a potientiometer inside the housing - essentially the same functionality as a rheostat.
You'll have to find way in there and hopefully find a chink in the pot. that you can spray some elecrical cleaner/lubricant through which should clear the problem.
I read some really good instructions on how to get into something if it "snapped" together as most modern plastic casings are these days, along the lines of "prise and pull until something gives slightly and you can tell where the snap fasteners are, then ease it apart" etc but obviously this method might be prone to failure.
Considering that you say " . .the volume changes to an extremely loud level by just touching the dial. . . . impossible to achieve the right volume . . " you may be better to seek a replacement from Dell if you're still within warranty.