My mouse doesn't turn on or charge.

It could be the charger. Try using a different one. If that doesn't work, take it apart and check the connections.

I have already had it open, I have done tests and the original works. I tried another one and it still doesn't work. I tested the battery with an object and it showed that it was good, but it still won't turn on. How strange.

Uhm.. what does "tested the battery with an object" mean? The image it brings to mind is shorting the terminals with to produce a spark... which is both dangerous and not indicative of a good battery, check it with a meter instead and if there's a part number on it, look it up on the web and see if you can find it, assuming it checks bad. I'm using a fantech venom with a battery that I replaced in this way... I think it's the first time I've had a mouse live long enough (not worn out physically) to actually need a new battery. (FWIW I've not had a Logitech mouse survive long at all... except the ancient trackball.) While you're using the meter check that the switches actually 'switch' (continuity open and closed) especially the on-off one, obviously... they are usually the first things to fail. (can be fixed but a pain)... Good Luck.