Replacing Adapter Sony VGN-AR71M Help

Hello,
So i just discovered that the laptop wouldn't switch on because it is out of battery and that is due to the wire coming away on the VGP-AC19V16 power adapter.

Electrical Tape has not helped the matter, i think it's protecting itself from frying the thing.. or i'm hoping it already hasn't.. It's my mum's laptop. When i push the on button, the button it lights up and remains lit so long as i hold it down (green LED) but there is no activity or signs of a boot. Since my little sister was using this last i'm guessing it's because the battery has now run down fully and it doesn't have the power to boot? But i'm now starting to worry more that it has fried it.. When i plugged the adapter in and fiddled with it i did manage to get the green light to come on sometimes on the adapter itself but that still wouldn't power the laptop on.. So i'm hoping and hoping the laptop is ok!

It's not good timing because tomorrow i'm flying to Sweden.. So now i've been looking for an adapter to replace it with.. I can't find any which are the exact same model:
Sony VAIO VGN-AR71M Charger Power Ac Adapter

But i found this:
Sony Vaio VGN AR31 Bärbar Dator Batterier, Laddare och Adapters - Bärbar dator Litium ion 62KM5R, A
The part which you put into the laptop (pin?) to provide power is straight and not a right angle i noticed, but it looks about the same size fit,
will it work? And how do i know the laptop aint fried?

Thankyou

Ok, so removed the battery and placed it back in properly and it is booting! woohoo now do i dare plug the faulty adapter back into the laptop to see if it will charge and the tape has done the trick?

Ok so i've answered my own questions now.. So long as the green light is on the charger is working haha and it's powering the laptop.. although a little tug on the wire can turn the adapter light out / off... Sorry for the bother!!

 

Double post. sorry!