Random shut downs - would really appreciate some help with this!

Hey everyone.

As the title suggest I have random shut downs on my Mac. I’m by no means a whiz with macs but am confident enough to take it apart and attempt fix suggestions myself.

Heres what I know -

• Macbook Pro 15” 2.66 i7 mid 2010 - yes it’s pretty old! It’s running High Sierra 10.13.6 which was the latest version until the point it can’t be upgraded due to the macs age.
• It randomly shuts down. It will do this when on battery or connected to mains. It will do this sometimes after it first starts up or sometimes after I’ve been using it for a while.- yesterday it did it 4 times in half an hour but then let me use it for 4 hours no stop! It can shut down when I’m simply browsing on chrome or when using apps such as Lightroom or Photoshop. I have noticed that I can leave it on (like when I’m backing up) all night and it won’t shut down- it seems to be when I’m using it mostly.
• The Mac has a Newertech battery installed. I’ve tried swapping to the old one and it still has random shut downs.
• The Mac had a RAM upgrade about 6 years ago. I haven’t tried swapping this out as I doubted this would be causing the issues. Plus I don’t have replacement RAM to try.
• My friend had a spare hard drive cable that I swapped out yesterday. The Mac still did random shut downs. They weren’t as frequent but I don’t really read much into this as they shutdowns are super random.
• Talking of the hard drive, it has been upgraded to a Samsung SSD 850 evo 1TB which was installed about 4 years ago. I’ve never had problems with the ssd itself and I tried swapping to the old spinning hd too which still performed the random shut downs.
• I’ve also completely wiped the Mac and re-installed everything and that hasn’t worked either.
• ive also tried resetting the SMC and the NVRAM too. Also I got rid of some random apps that were enabled to start on boot up just in case. 
  

That about sums it up. Like I say I’m no pro with macs but slightly better than the average person! Any help would be awesome as I can’t afford to replace it right now. Thanks in advance!