Battery problems after replacing lightning assembly

About two weeks ago, I replaced my iPhone's lightning connector and headphone jack assembly. This solved the problems I had been having (lack of response to earbud in-line remote, and earbud audio cutting out when I pressed the Home button), but new, more severe problems immediately emerged. My phone would sometimes turn itself off and then back on several times in quick succession (this problem seemed to toggle when I manually turned it off and on), and the displayed battery charge appeared completely unreliable. The lightning bolt icon would appear when I plugged the phone in to charge, but because of that unreliability of the reported charge, I have no idea whether it ever actually charged. A few days ago, it shut off and simply would not turn on again, whether or not it was connected to power. At one point it briefly displayed the Apple icon when I applied pressure near the battery connector.

I suspect the problem is that the battery is not connected to the logic board correctly. However, other problems I encountered while reassembling the phone included difficulty connecting the antenna (on the lightning assembly) to the logic board (I noticed that it was originally held with a small amount of glue) and difficulty keeping the lightning cable connector attached to the logic board (I successfully plugged it in a few times, but it would detach a few seconds later without apparent cause).

I have also noticed that the lightning assembly which I bought from iFixit is missing a foam pad on the panel which connects to the logic board, and that the store does not appear to sell these separately (as the only foam pads I saw listed for the 5c were for the audio control cable connector, battery connector, digitizer connector, and LCD connector). Would one of the other pads be an appropriate replacement? If not, is there some way I could remove the pad from the old lightning assembly and apply it to the new one?

I would like to know whether my current assumption (battery connector problems) matches up with the symptoms, and whether anyone has any tips for keeping the antenna and connector from the lightning assembly connected to the logic board. Thanks.

Edit: I have padded the lightning assembly connector with masking tape and verified that both it and the antenna cable are securely connected to the logic board. I also disconnected and reconnected the battery to the logic board. Nothing seemed obviously wrong, but when I plugged the phone in again, it shut itself off again a few minutes later.