Need a replacement battery for my Logitech MM50: It is a GP Li-lion Battery, part no. NTA2335, 3.7 volt

The first thing you could do is trying another charger of the same type, if the battery starts charging you'll only have to get a good charger, if it doesn't, you have a failing charging jack, circuit or battery at portable speakers.

It's probably the power adaptor at fault. You can find a replacement 12V power adaptor here: https://www.digidave.co.uk/jshop/product.php?xProd=4762

go to this link and scroll just past halfway down. It's not all THAT hard but an exact replacement is not available.
http://forums.logitech.com/logitech/board/message?board.id=general_speakers&thread.id=26

Try either eBay, or go to Radio Shack.  You'll find them there.

take out the battery

I am 100% sure the battery is dead.
Opening my mm50 I find that the small 2"X 1/4" battery is attached to the back, very near the charging socket. The battery is connected to the circuit board through a small plug-socket arrangement - no soldering here like iPod. So, it would not be difficult to replace it by a DIY enthusiast. But it would be difficult to find this non-standard replacement battery. Better leave the job to Logitech service, they'd would certainly replace it on charge basis.
=Subhas Chatterjee=

The battery for the MM50 speaker is VERY hard to find. Logitech does not make a replacement battery for this unit but here is a link to a site that carries it: Replacement NTA2335 Battery for Logitech MM50 iPod Speaker
The battery has a plastic connector which connects to the board so soldering will not be necessary. You just open up the back and switch it out. Easy Peasy!

if no light came from the speakers then something is corrupted inside them .. you have to check the power source and power cable of the speakers first ... if everything is fine then the speakers are corrupted from inside

yeh surely u can shop it via ebay itself

hey u r using speakers..so i think power is not suff for them to run..so use dc flug boards..i mean direct curr...
y do u try for a batery??itz waste of money