I had same problem on my previous computer, I had to short 2 pins on the motherboard for it to fix the problem, I can't remember what the pin is called lemme look.
i think your power supply is weak or has an issue, idk much about pc's but it shuts down way too early to blame anything else
Ohhh mine was due to bios issue, and set it back to factory default, not sure if it would help but look on motherboard near bottom right for 2 pins with CLR_CMOS and short them.
Maybe it shuts itself off deu to overheating, most computers are programmed that way. I see your vents are inside the desktop. Have you tried waiting 10 minutes or so before restarting it?
I still have a year return and fix with pc specialist, do you guys think it's worth fixing this myself or returning it to them free of charge?
Lol I am most definetely not going to try this myself. Last time I tried to fix something it was doing the task of simply replacing my iphone 5 battery, and I ended up cracking the screen in half :3 The battery didn't even end up working.
Instead of sending it back you should ask if they could try some things over the phone or by email. I had pictures emailed to me and sorted my problem out.
Make use of warranty while you have it. It's dumb and stupid to do it yourself and risk losing warranty while you still have got warranty.
Try pushing on the cables from the power supply back in. Mine did this and it was a loose connection to the motherboard.
try replacing CMOS Battery, or do what Rejected said and find the Short pins on your mobo with a quick google
Okay so what I figured out so far, is that it's either a short somewhere, or the power supply. I did a troubleshoot on the graphics card and ram because they are easy to remove, and I also reset the small battery thingy but that did nothing. It could be a bios thing but going by the stats below, I know that only 80% of these things are accurate but mine seems a bit off.