I recently replaced my iPhone 5s digitizer/screen and everything works fine but now it seems like the battery drains...

So after much significant frustration I found that software issues were to blame surrounding the iOS 7.1 release that occurred around the time of my screen replacement. It wasn't a short in the hardware it ended up being processes running constantly. Under settings my usage and standby were almost identical times. No typical fix helped because the corruption was in my backup as well. I only fixed it after a factory restore and setting it up as a new phone. But the upside is the screen is fine and was not the cause of the battery drain.

Haven't resolved the issue as of yet. But I do agree that some sort of short is very likely. Especially with all the other typical battery drain issues having been tested(brightness, bluetooth, background app refresh, Etc... Not convinced it isn't the replacement screen though. If there was a minor short in the cabling it could still cause current drain even if the battery cables are fine. Parasitic drain could likely come from many parts of the phone if there was a short within a given component.