Sounds duff, but just a "last ditcher" - did you leave it charging on PC/laptop overnight, say ?
It is possible, should your computer have an auto close-down, that it drains the battery. If you have a wall charger with a plug that fits - but not anything Apple related, they aren't good - might be worth trying that.
Or, just bung it back, which might be the best solution.
Don't forget, if you're in UK, unless you bought it from Sony direct, your contract is with the retailer/supplier who supplied it, and they have to replace/refund/sort it out. If they tell you to contact Sony, tell them that's their job...
This also applies to Sony Centre's, by the way - who, strange as it may sound, are nothing to do with Sony Corp !
Quote the "Sale of Goods Act", and they should realize you're not to be messed with. They are liable under the law.
'Course, if you got it from Sony, the situation is the same, but the process won't be quite so hands-on ! See your PM's.
Good idea to look up the Act, which is a terrific piece of consumer law, if you're unfamiliar, first.
"WHICH" , I know, and the Citizen's Advice Bureau I imagine, do a very easy to read explanation of your rights under this act of law, but you'll find a number of brief run-downs if you Google it.
Good luck.