The culprit is this guy below
Very nice piece of furniture I snatched for just $100
But boy, it came with an "old" odor! I tried painting the drawers
It smelled like fresh paint for a little while
A "little while" is right....It's back to smelling old again
So I researched different ways to get rid of that musty smells in furniture
And this is what I found
1. Clean the drawers out well with a damp cloth
2. Let it air out/dry in the sun for a while (maybe several days)
3. Sprinkle baking soda everywhere and let it sit for several days. Vacuum and repeat this step if necessary or maybe leave a small box of baking soda open in each drawer until the smell is all gone
4. Line each drawers with dryer sheets and let them work their magic for several days if the baking soda does not wrk
5. Pour coffee beans inside to absorbe the odor is another good alternative
6. Place a few small bowls of white vinegar in each drawer and let it absorb the smell. The vinegar smell won't linger
7. store scented candles or soaps in the drawers
You might have to repeat any of these tricks several times.
Let me know if you have tried any of these and if they worked.