I would have to agree with Flying Dutchman it's not worth putting any money in or time since you can buy a new for less but I strongly recommend fluke meters if you can they are roughed reliable and accurate. It sounds to me that the logic board is bad and needs to be replaced.
@cois Is there still functionality when reading the meter is it just the continuity .Is there continuity functionality , what reading are you getting with the leads not connected and connected, if all other functions are OK don't throw the baby out with the bath water. I agree with Flying Dutchman in that you need a multi meter to test this one . I have a drawer full of cheap multi meters (family seems to think its a good fathers day gift)and I use them all I have an expensive Snap on multi meter and I tend to use the cheap ones more often.
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!
I have an expensive Sumo DT-61 and it is having the same problem especially after i accidentally tested a charged 400 volts capacitor for dc voltage output of an electric mosquito bat/zapper which created a spark onto the lead probe but despite that all other tests are still working except for diode test, continuity test with never ending long beeping sound and ohm mode. My multimeter can accept up to 600 volts max for dc voltage test so I don't know why it is causing this issue. The fuses are also working and I had also changed the battery. I don't know if this is a chinese multimeter but I think that Sumo Industrial is either a british or scottish company based in Glasgow, UK and this multimeter is the most expensive one in the store since it is also an environmental multimeter that can measure noise, temperature, electromagnetic frequency and light. I think that I better RMA it.
