Random crashes - stock lenovo laptop

Hi everyone,
I'm trying to help my brother remotely. He has a stock Lenovo T440s. It's about 14 months old. He was having all sorts of random issues so about 6 weeks ago, he requested I do a fresh rebuild, hoping it would solve the problem.
It hasn't.

Can you advise me the best way to proceed?
What tests to run or things to investigate. This is a business - use laptop- no gaming or things that (should) stress it.

It's running Win 7 pro, outlook 2013, Firefox 35, 8 GB RAM, i7, onboard graphics.
Let me know what else to provide and I will.

I was thinking a memtest would be useful- which is the best test - note he has to run it, so it should be easy :)

I would like some program to be running in hte background, to record errors as they occur. I don't think that they are reproduceably on demand.

thank you. I don't know where else to turn, so I appreciate your help and handholding.

HI, I'll install speccy tomorrow am.
It came with win 7. I think he might have paid more for that config. When I reinstalled win 7 a few weeks ago, I wiped the drive, and got all the drivers from the lenovo site and used the lenovo update manager to get a lot of them.

I ran HCI memtest over night. It was over 800% coverage with 0 errors so we stopped it.
Will look at the temps next.

Thanks!

In addition work through these Troubleshooting Steps for Windows 7.

Compare the reinstall you did with the perfect install compiled in Clean Reinstall Windows 7 in particular how drivers are handled. You may want to do it over.