Strange behavior
I had a similar problem with the 108 module, when i pressed the lightbutton, the display would go off, and there was a brand new battery installed.
The problem was the battery, although it was new it didn't have the strength to power the watch properly.
I don't know if that is your problem as well, but i found out that these modules are sensitive to batteries that don't deliver enough power.
I bought a professional varta battery for my W-250 marlin (108 module), and had no problems anymore.
PS. is the right battery installed (CR2320)? , sometimes people install a CR2016 because they don't know what to intall. This can give problems too.