Did you used the right displays. Yhere care common anode and common cathode displays. Here you need common anode. But in that case it probably would show nothing.
Biggest change is you made some fault or there is a bad solderjoint. But with only this schematic my crystal ball stays dark ;-)
Have you checked the datasheet ? There are more versions. The 7107 has a different pin out as the 7107R. This is a very much and very long used IC . Fluke made a multimeter with the 7106 LCD version of this IC. (Fluke 8020 ).
Edit: I'm sure it can not be the code because there is nothing to program. The 7107 is a Voltmeter IC.