When you have a particle board set of drawers, it usually doesn't last long because weight on top will bow the top, and it cannot handle much "side to side" stress. To strengthen it up, get the weight off and remove the drawers. Then, remove the back so you have just the skeleton. Then, make some U-frames out of 1x2 poplar wood. Put 4 or 5 frames inside ... one in the front, one in the back, then 1,2, or 3 in between. Making them like U frames means you can get away with minimal screws ... use glue to hold the top piece on, then put the side pieces on and secure with glue as well. Make sure you put the side portions of the U frames UNDER the top piece. Anyway, once dry, put in screws into the bottom on each side. At that point, it will hold LOTS of weight on top.
Now you need to fix it so it won't move side to side. Go into the corners, just the top/back is fine, and secure in 45 degree pieces of wood at the top corners using glue and nails as shown below. I usually use 6" pieces of 3/4" plywood ... plywood is best because it doesn't split as easily.
Once those two steps are complete, it will be super strong.
