Don't be afraid to tell TWC that you want your own dedicated drop line running from the street trunk directly into your apartment. In most states they are required to provide the same service to both privately owned and short or long term rental dwellings. It doesn't matter that they might have previously negotiated a long-standing exclusive cable service agreement with the MDU building owner or homeowners association. You can contact your state's Public Utilities Commission for more information.
This sounds like buried splitters or directional couplers between daisy chained wall jacks, You need to see if there's more wall jacks in your suite and what's behind the wall plates especially if the modem "sorta works" when connected to them.
Empty active jacks must have terminating resistors screwed into them.
. Many techs have no clue how a building was or is wired and do not have proper equipment to determine how far along a cable fault is....