I just got an LP-3000 as well and had the exact same problem. I found that by adjusting the tonearm height to 4.5mm from the mat to the tip of the stylus ( as specified in the manual ) it worked fine. If the arm is too high, the sensor in the headshell can't pick up the reflections from the record and will think no record is on the platter so won't stop or lower. The height control is the small knob at the front of the tonearm base on top.
You'll also probably need to replace the rubber belt that drives the tonearm lateral movement as it will work fine at high speed but will slip when playing if the belt is old.