MacBook powers on, CPU fan spins, Bank Screen

My A1405 MBA has been somewhat neglected for a while and I recently went to use it and found that, when powering it on, the CPU fan would slowly start spinning faster and faster but nothing else would happen. No boot sound, no keyboard lights, nothing.

I’ve tried resetting the NVRAM, PRAM and the SMC. There is no audible feedback from the Macbook when doing so.

Thinking it was the battery, I removed the rear cover and disconnected it, plugged in the charger and had the same experience.

Is she dead? Is it worth trying to replace the logic board? It’s a 4Gb RAM, 1.5GHz i5 so it’s not much to write home about but I still love it dearly!