I saw a suggestion by a user on the Dell support site to try booting from a USB stick.
I'd also suggest booting from a DVD or other device.
Disconnect all attachments. Normally, this is a suggestion suitable for driver-level problems.
Since the power light comes on, somebody's home. I suggest adding an external screen (VGA, HDMI, DP etc) in case it's simply failing to reach the laptop screen.
Delving deeper, plug in a simple working hard-drive in place of the built-in one.
It's certainly the responsibility of Dell but that takes time and effort.
A replacement or re-flashed BIOS chip should fix this, rather than a new motherboard. Swapping a motherboard is a non-trivial task.
What's the second-hand market for such machines?
Disclaimer: I've been very pleased with all my support from them in the past.