Hi i bought two LCD's 16x2 and they worked fine initially. One was with backlight and the other without it. The one with the backlight worked fine once and then the next day it wasnt showing any thing. When i adjusted the contrast it showed squares in only the 2nd row.About the one without backlight it doesnt show anything at all(no squares or anything0. Both of them get warmed up(the black blobs on the back get slightly hot).
As said provide a diagram. What is controlling the modules? If it's a microcontroller then try to supply the code you're using. Your description doesn't sound very encouraging, but there's still hope, and at least they're very cheap to replace.