I have the same problem. When this device is connected to USB I too get the "open" and "close" sound constantly.
This part gives me some hope: it seems like you may be having an issue with your Digispark connection to the computer.
Recently, I was going through some old posts, looking for an answer to another issue. It seems that some times the USB does not connect very well. From your description, this may be the issue here.
Digistump suggests trying using a hub (I tried a cheapie hub given at a trade show, which worked for my issue.) I also remember back in the beginning of USB, some people had troubles with just using the PCB traces as fingers in the USB connection (like the Digispark has.) They did not make good connections to the USB socket. First, try using a hub, if that does not work, try using a pencil eraser to buff the exposed PCB traces on the Digispark USB connector to clean off the oxidation. Finally, if that also does not work, try to add a thick layer of solder (1/4 mm or so) to the traces, to thicken the connection a bit. Be careful to not use too much heat, or you may lift the traces off the board. Also, you need to scrub the rosin off with a stiff bristle brush (like a tooth brush) and plenty of alcohol.
Try that, and let us know what happens.