Mac Pro Tower, randomly hanging convinced its a hardware problem but Apple think otherwise Just about ready to launch this machine out the window it's driving me crazy.

Ok so a rundown of what has happened thus far.

Bought a Mac Pro Tower around 2010, worked like a dream for 3 years then due to circumstances it had to be put into storage for the past 2 years.

Anyway when I got it out of storage a few weeks ago and fired it up I noticed that it keep randomly hanging and nothing would allow me to resume control. Due to the age of the machine I figured it could have been a failing HD, so replaced it with a new one and done a clean install of Snow Leopard. 

That didn't make any difference, so after asking around on here I got told it could have been the PRAM battery, so I then replaced that too and again it made no difference.

At that point I took it into the Apple Store, it crashed twice when they loaded their own OS on it so they kept it in for further investigation. They then called me up to say that they couldn't find any hardware faults but that they did install a newer version of Snow Leopard.

So I have just got it home, set it up and it crashed yet again.

Any ideas what I should do now?
Yes - troubleshooting this could be easy if you take some time. Get a notepad and write down the times of the problems - day, minute, second. Over time a pattern will emerge.

Save the logs - after it crashes - run the command sudo sysdiagnose as this will package each crash and the logs for later analysis.

Pay attention to what crashes - is it a kernel panic, a freeze, an abrupt reboot. The steps to diagnose each is slightly different. We have a [chat] for getting troubleshooting help if you need a start.