LCD working, but Digitizer not, how do I diagnose?

I have replaced the LCD/Digitizer assembly 2x on my iPhone 5c. In both cases I have had the following result:

the LCD works. I can see the screen. The home button functions when pressed allowing me to see the apps and, for the lack of a better word, the dashboard. The touch function does not work despite being able to see everything. Additionally, after the screen times out and I reactivate it; the screen starts out dark and then lightens as it “fully engages” for the lack of a better phrase.

I attempted reseting via iTunes and was successful; however, this did not fix my digitizer issue or the screen lightening issue the latter being perhaps a minor issue.

I talked with a phone repair techs at one of those phone repair booths and they mentioned that what could have happened is that the battery could have sent a charge through the motherboard and shorted the digitizer. I am unsure if he meant the LCD/Digitizer assembly or the digitizer part on the motherboard.

So now I am at the diagnosing stage. I think the cost of having them diagnosing is roughly $30, I was unable to listen completely as I was carrying my toddler. BUT how would I do the diagnosing? How can I figure out what is wrong with my phone?

Should I just attempt another LCD/Digitizer assembly, if that doesn’t work though what then? how can I trace the problem?