'Seemingly' dead Lithium-ion Battery...charge time?

[equippedbum]

Mon. night I listened to my Sony ZX2 for roughly 5 hrs...everything sounded awesome.

I went to charge it that night and I left it plugged in overnight. Next day it was still at about 50%, so I plugged it in again but it didn't show it was charging (first time this had ever happened) 

It drained to 0% and hasn't been able to turn on since.

I connected it to my computer and it doesn't show in Sony Media-Go ("No compatible device is connected") It did also when it had power to boot up...still not recognized in Media-Go

Is this a battery issue? A cable issue? Would a dead battery cause the device to not be recognized?

The same wall socket and USB port charges my phone/ipod etc. with no problems. 

I'm just about to order a new cable...was looking for any other troubleshooting tips before I order it. 

Thanks in advance!~

EDIT: I've heard it can take up to 48 hrs for a dormant seemingly dead lithium battery to even start charging...is this so?

I left it plugged in to the USB port all night and then plugged it in to the wall socket for 18 hrs. and still nothing. Wont turn on /won't hard start etc.