My daughters sony laptop GR370 power went out shortly after using an aftermarket power supply. Now when it is connected, there is no sign of activity/lights etc. What most likely went wrong and would likely need replacing?

Sounds like the power supply itself failed or it was not compatible with the board.
The voltage might not have been correct.

Are you saying that you installed this new power supply & then the machine just stopped working?

http://www.google.com/search?q=sony%20laptop%20GR370

No, the charger still works. When it is plugged into the laptop, the indicator light is on, but waxes and wanes in intensity. The computer however is just dead with no lights on.

Sounds to me like a dead battery. Have you tried an AC adapter?

http://www.ebatts.com/sony_vaio-pcg-...cessories.aspx

also

http://esupport.sony.com/perl/model-...PCGGR370&LOC=3

yes...that's what I mean. I plug the AC adapter in and hit the on button but there is no activity with the laptop.

What Jephree was originally saying sounds right - the AC adaptor might be incompatible with the laptop (wrong volts or amps). If you look on the underside of the laptop, there's normally a label stating what power requirements it has. If it's not the same as what you plugged in, then it could have damaged any number of internal components. If it's all the same, then you might just have a duff power adaptor.

P.S. When you say it was an "aftermarket" one, was it a Sony power adaptor specifically for that laptop range or was it one of those "universal" ones where you can change voltage, etc?