By battery cable I assume you mean the adapter? If the adapter and battery work fine in another laptop then it could be either a DC jack on the laptop or the charging circuit on the MB but like you I am leaning more toward it being an MB problem.
I have a Dell Latitude e5470 that I purchased used a couple years ago.  It worked well enough until just recently.  Now, while the laptop recognizes the battery, the battery won't charge (it's "stuck" at 62%), and if I unplug the laptop from power, it instantly dies as if it just had the only power source pulled.  The issue has crept up a bit as opposed to being a sudden failure, as it would previously randomly die while on battery power occasionally, and then occasionally got to be more often until now when it instantly dies when I pull the plug. I know the issue isn't the battery because I purchased a new (Dell OEM) battery while the issue was still intermittent and both batteries exhibit the exact same issue.  One battery is currently at 62% charge and the other at 68% charge, and the laptop will not charge either of them further, nor will the laptop work off of either battery.  I even tried the battery in another laptop (including the battery cable in case the cable might be the problem) and it powered the other laptop with no problem.  So the issue is definitely localized to my laptop.   At this point, I'm kind of resigned to the conclusion that I have a bad charging circuit on my motherboard, but figured I'd post here on the forums to see if anyone has any other ideas before I purchase a replacement and sell this one as "works great while plugged in".   Thanks in advance! -Doug
Dell Latitude e5470 battery issues, but it's not the battery