I thought I'd take a stab at this but if I am way off or no help at all, please accept my apologies.
I am only posting because I think I have read this question before on Ubuntu forums. The answer is often to check the 'Mixer' or the graphic equalizer. In KDE, it's KMix but I am sure that Gnome has something similar. I would check the equalizer/mixer to see if sound is muted.
Also, maybe post what your internal sound card is (in the D420). You can probably figure it out (if you don't know it already) by typing the command, 'lspci.'
Does your sound work if you run a Mint Live CD? If so, maybe something got corrupted? I know some Debian distros have alsaconf so what is Mint's equivalent sound configuration software tool? (I'm asking Mint experts. ;- ) ).