New Inspiron 5423 unexpectedly restarting

Hello, I wonder if anyone can help me, I'm at the end of my rope on what to do next, particularly as I'm currently living overseas and my computer is my lifeline to my family back home and my work (which I do online).

Specs

1. New Inspiron 5423
2. i7-3537U 2.0GHz
3. Bios Dell A10,1/29/2013
4. Graphics: AMD Radeon HD 7570m
5. 250GB static HD

After having my new inspiron for about a week, yesterday it just started unexpectedly restarting.

It came with Windows 8, but for my work I needed Windows 7 - so I installed that and continued to install all my usual programs. Windows 7 was activated and I had downloaded and installed all updates available.

So when it first started rebooting, I restored it back to the previous day (last know good configuration), but the problem continued to occur.

I did the dell startup diagnostics (even the extra mem tests) and there were no error messages.

I decided to reinstall windows 7 from scratch, and it was ok at first, but then after a couple of hours it started happening again.

I can load in to Safe mode with networking (what I am currently in) - and it seems to be fine, I haven't experienced a reboot in safemode.

I downloaded coretemp - and it doesn't seem like a temperature issue as it's restarting, not shutting down - and it showed the chip was running between 56-64 degrees which seemed normal.

From what I can tell, it's not any particular program I've installed that is causing the issue. 

I don't think this could be a virus due to the clean installs (and having mcafee installed).

I installed Turned on Times View (nirsoft) - which gives you a list of when and why the system was turned on/off, if it can. Eg when you restart for windows updates, the log shows that it was a planned restart etc. However after my system unexpectedly restarts, there is no reason listed.

Can anyone offer any advice on maybe how to figure out what is causing the restarts?

I'm not even sure where to go next - should I be looking at the drivers, could they cause this? Or am I looking at a hardware failure? I tried to look at the Event Viewer but to be honest I'm not really sure what I'm looking for.

Any guidance would be highly appreciated!

Samantha