Since Dell does not support Vista on that model you will probably have to do what others who have upgraded "older" systems that are not supported by Dell, install a PCI sound card that is Vista compatible.  If you can find a SoundBlaster Audigy SE sound card ($30 and used to be even available at Wal-Mart), it will support Vista and about the least expensive option.  
i have dell dimension 4600...and upgraded from xphome to Vista home basic. it seems working fine but have audio problems. PC produces no sound... i checked device manager and sound driver(soundmax integrated digital audio) seems ok.. but there is two "!" sign at "other devices" on Multimedia audio controller and PCI Input device. those two "!"drivers cannot be updated or not recognized....hmm!! i couldn't find any drivers updated for VISTA at dell drivers list either. help me!!! i want sound!
upgraded from xp home to Vista Home Basic