I have a cheap Chinese multimeter UNI-T 132b and while I was unknowingly measuring currents way above 200 mA (the chosen scale) it just stopped measuring anything. The other functions worked like charm except DC small currents and diode/continuity. Similar to your situation, leads or not it kept on beeping while testing for continuity. Opened it up and found that the fuse for that circuit was gone. I temporarily 'replaced' it with some plain wire to test the multimeter for further damages. Beeping stopped and DC small currents measurement worked just fine. So that's like an error beep or something. Bought a new fuse for under a dollar and my multimeter is as good as new now. Hope you have the same luck!