logicboard or battery

It is really hard to say as these USB-C Macs are very quirky. The Battery is the weakest link here. The important information would be whether the Apple tech disconnected the battery and tried to power on the laptop using just the charger. It is not 100% definitive, but if it powers on, then the battery is most likely bad and the cause of the problem. A bad battery can prevent a Mac from powering on or even charging. Now, disconnecting the battery may or may not allow the laptop to boot as this seems to vary from machine to machine (may boot extremely slow) -- again the quirky nature of these USB-C Apple laptops, but the important part is if the laptop powers on at all.

Of course the 2016 & 2017 MBPros have a known design flaw with the Display Assembly which can sometimes cause the backlight to fail which will make the laptop appear like it is not powered on since there are no indicator lights on these Macs. The problem may be intermittent. You can try pressing the Caps Lock key to see if its LED lights up which indicates the laptop is powered on.

Unfortunately I have seen USB-C Apple laptops suddenly not power on at all (seems completely dead) after performing an SMC Reset followed immediately by an PRAM Reset. In this case, I have sometimes found disconnecting the charger and reconnecting the charger will trigger the laptop to power on, other times I waited five minutes and the laptop powered on automatically by itself (battery had a good charge). Yet the user never mentioned any power on issues and everything else checks out fine. Like I said, these laptops are very quirky.

It is also possible the contacts on the USB-C ports are oxidized or even damaged from a bit of liquid. I find a lot of our organization's Apple USB-C laptops with liquid damaged ports as all it takes is a single drop of liquid. Unfortunately you cannot always see corrosion on the contacts (requires actually removing the Logic Board to get a good view of the contacts). The 2016-2017 models also have very badly designed USB-C ports where they become loose where the cables won't fit tight anymore (design flaw which Apple rectified with the 2018+ models). With the non-touchbar model, the USB-C ports are integrated into the Logic Board (yet another poor design decision).

A battery replacement is about the only repair I will even consider for the 2016-2017 non-touchbar model since this model has so many known issues (bad Keyboard, bad Display, bad SSD, loose USB-C ports integrated into the Logic Board). I will only recommend this after I carefully examine the laptop and verify the USB-C ports are still in good enough shape to keep the USB-C cables in place.

If the Genius Bar got no signs of life whatsoever from your Mac I can't really fault them for concluding it was simply dead.

Since you resurrected it, their diagnosis appears to have been premature. They didn't spend much time with you, and a more thorough diagnosis might have revealed another cause.

Did you try a SMC Reset? Reset the SMC of your Mac - Apple Support

Try a different power adapter or cable if you haven't already. Refer to Identify your Mac power adapter - Apple Support. Notably, an archived version of that same document contained a passage that was helpful in identifying potentially faulty USB-C cables, under the heading Make sure you're using the correct USB-C charge cable. See if it's applicable.

A completely discharged battery or a battery with issues can prevent an Apple laptop from powering on at all or even charging. Many times I must disconnect the battery to power on an Apple laptop, after which I will hot plug the battery which usually allows the battery to charge if the battery had been completely discharged. I cannot believe a tech would not try disconnecting the battery. I almost always remove the Bottom Case just to check for possible swelling of the battery and possible liquid damage since I know that Apple has a secret free repair program for swollen batteries (must be less than three years old -- we've had several swollen laptop batteries replaced for free on two year old laptops -- may vary by region and tech's knowledge of the program).

The non-USB-C Apple laptops were easier to diagnose here compared to the USB-C models where other quirky behavior makes it much harder to be sure of a diagnosis, although I have developed ways of detecting battery issues while monitoring the battery capacity while quickly discharging & charging the battery which can reveal issues (Intel only at this time since Apple has changed things with the Apple Silicon Macs).

Make sure not to leave the battery at low charge levels without connecting the charger. Apple laptops tend to have problems when the battery is at 0%, or even at 10% or less when the battery is wearing out/failing. Besides, leaving the battery at 0% charge for too long can cause permanent damage. Another quirk of these Apple USB-C laptops is they will show the battery symbol even when the battery has sufficient charge to run the laptop, but for some reason the laptop wants/needs to have the charger connected before it will power on the laptop. Crazy and annoying behavior.

You should always have frequent and regular backups of your computer and all external media (including the cloud) which includes important & unique data.

Good luck.