Colin Marson , I take it worked on the new battery till it died and now refuses to charge. Did you check the port and blow any dust/debri out of port. Look in port and straighten any bent pins with tooth pick very carefully. Still no go, remove battery door and with a DVOM with charger plugged into device check plug at battery to see if charger is sending voltage to battery, if not probable loose/bad charge port,change the charge port. the link below is a tear down guide that can get you access to the charge port which is soldered to the mother board and is not a job for the newby because of the fine components and heat involved. 2nd link shows a charge port being resoldered.Good luck.
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Garmin nüvi 3590 LMT Circuit Board Replacement