I would recommend trying a trackpad cable (£10), if the trackpad is not recognised on the 13" 2015 models, the keyboard will not work at all.
On this model in particular, I have seen a lot where the cable intermittently fails (keyboard and trackpad sometimes works, sometimes doesn't) and it sounds like the periods where you can't boot is where the trackpad cable is acting up.
I have seen these with your exact issue, ones where it will randomly act up whilst switched on or when sleeping/waking. It's a cheap part, try that first, then I would recommend taking it to a repairer who will have the test parts available, so they can easily diagnose this properly.
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