I build my own computers, and the quietest cases I am aware of are some of the Antec's, including the P180 and P182 models, and possibly (although I'm not certain) some of their more recently introduced models.
You might find this site of interest:
http://www.silentpcreview.com/If you don't build your own computers, there are lots of custom builders out there, findable on the web, who I'm sure could make a very quiet computer, using these or comparable cases. You might also want to consider transferring the innards of your present computer into one of these cases, assuming that:
-- The computer is reasonably contemporary and performs satisfactorily.
-- The computer uses a standard ATX motherboard (Dell's, in particular, often use non-standard motherboards, and possibly power supplies as well, that will not fit into a standard case.
-- The computer's internal noisemakers that are not part of the case (cpu fan, hard drives, power supply, video card) are not unreasonably loud, or would be replaced with quieter counterparts.
Regards,
-- Al