Mid 2014 MBP Logic Board issue?

I have a Mid-2014 MBP (A1398) that I've been using as my main laptop for almost 2 years now (Yes, my budget is that limited) And I was intending to replace it this year, by selling it on to put towards a new(er) laptop.

Anyway to cut a long story short, I went to turn on the machine to check to see if it was ok before packing it up ready for sale when mid way through the boot chime, the MacBook shut down suddenly and now won't re-boot at all.

I've tried the usual, reset SMC, didn't work because the magsafe didn't turn green, tried resetting the PRAM for what it was worth, tried powering up the MacBook without the battery plugged in and nothing. I'm certain that the Logic Board is at fault, but I just want to exhaust every possible option I can before I give up and write it off as a parts machine.

If anyone can give me any ideas as to what I can try, I'd love to know. Thanks.

Additional information: the machine has a 2.2GHz i7-4770HQ, Intel Iris Pro graphics and 16GB RAM with a 256GB SSD.