What Soeren meant was one lithium cell is 3.7v you said 3.7-7.4v...
Lovely when other people try to formulate what you meant, disregarding any factual knowledge thereoff blackbeard
<- I simply ment to take measures, which you obviously did (but forgot to mention
If it's impossible to get specs from the manufacturer or perhaps a forum about such stuff (search for your model + "battery" or something similar), try hooking it up to a variable supply.
It's most definitely a lithium based battery, as they are the ones used in such stuff and they're the only types that can be formed into any shape. I'd bet a dollar to a dime that it's a single cell lithium, so it will probably run from at least 2.5V to 2.9V, perhaps lower so start at ~2.0V and increase 0.1V for each test until it work without errors when buttons are pushed and at max. volume (don't plug it in your ears while testing this!)
If you post the make and model as well, perhaps someone here knows the model and can help you further.
Remember, the more info you provide, the greater the chance that someone can come up with an answer.