RV Repair: RV wiring, fleetwood tent trailer, rv wiring

Question
My fleetwood tent trailer has a problem with the 12 volt wiring. The battery was dead. Had it checked and was told it would not hold charge.  I bought new battery but before hooking it up wanted to make sure something in trailer wiring was not causing battery failure.  I found a burnt and broken pin on the connector between battery and trailer harness,  from positive terminal.
My question is, should I be getting continuity between black and white wires on trailer side,  battery disconnected?  I have about 3.4 ohms.  I do not want to connect battery until certain.  Thanks

Answer
as long as i am reading this correct.no you should not be getting continuity between the black and white.you need to trace them down and see if they are burnt together or if something has shorted out.also you didn't mention what colors on the harness was broken and burnt.if you need any more help just let me know.hope this helps.
thanks and happy camping don