I also experienced this problem yesterday. Update&upgrade -> reboot -> no HDMI output, red and blue LED solid on. The network interface LED starts flickering like an HDD LED, but after a couple of seconds it is being turned on and off with maybe 1.5s delay and nothing more happens.
Since I'm not the "deep into Linux" guy, I googled my ass off for a couple of hours, tried fixing things, upgraded my device to the dev kernels and uboots and I have no idea what else I tried (it was 4am in the end ;-) ). I did all that chroot'ing into the USB mounted SD HC of my original system after I set up a different SD HC with a fresh armbian installation and probably fucked up the whole original installation, but I learned a lot. :-)
Could someone please explain in a short version how I can downgrade the system to 5.35 to check if I completely messed up or if it at least boots? Upgrading wasn't a problem, since I could just use the kernel packages provided by the Armbian page, but I'm to dumb to find the ones to downgrade.
Btw: Here's the update history from yesterday before everything went wrong (maybe it helps):
Upgrade: libgcj16:arm64 (5.4.0-6ubuntu1~16.04.5, 5.4.0-6ubuntu1~16.04.6), libgcc-5-dev:arm64 (5.4.0-6ubuntu1~16.04.5, 5.4.0-6ubuntu1~16.04.6), gcj-5-jre-headless:arm64 (5.4.0-6ubuntu1~16.04.5, 5.4.0-6ubuntu1~16.04.6), linux-image-odroidc2:arm64 (5.35, 5.38), cpp-5:arm64 (5.4.0-6ubuntu1~16.04.5, 5.4.0-6ubuntu1~16.04.6), libitm1:arm64 (5.4.0-6ubuntu1~16.04.5, 5.4.0-6ubuntu1~16.04.6), libvdpau1:arm64 (1.1.1-10~armbian5.35+1, 1.1.1-10~armbian5.38+1), libasan2:arm64 (5.4.0-6ubuntu1~16.04.5, 5.4.0-6ubuntu1~16.04.6), gcc-5-base:arm64 (5.4.0-6ubuntu1~16.04.5, 5.4.0-6ubuntu1~16.04.6), gcc-5-base:armhf (5.4.0-6ubuntu1~16.04.5, 5.4.0-6ubuntu1~16.04.6), gcj-5-jre-lib:arm64 (5.4.0-6ubuntu1~16.04.5, 5.4.0-6ubuntu1~16.04.6), armbian-firmware:arm64 (5.35, 5.38), libstdc++-5-dev:arm64 (5.4.0-6ubuntu1~16.04.5, 5.4.0-6ubuntu1~16.04.6), libubsan0:arm64 (5.4.0-6ubuntu1~16.04.5, 5.4.0-6ubuntu1~16.04.6), g++-5:arm64 (5.4.0-6ubuntu1~16.04.5, 5.4.0-6ubuntu1~16.04.6), sunxi-tools:arm64 (1.4.2-1~armbian5.35+1, 1.4.2-2~armbian5.38+1), gcc-5:arm64 (5.4.0-6ubuntu1~16.04.5, 5.4.0-6ubuntu1~16.04.6), linux-u-boot-odroidc2-default:arm64 (5.35, 5.38), armbian-config:arm64 (5.36, 5.38), libgomp1:arm64 (5.4.0-6ubuntu1~16.04.5, 5.4.0-6ubuntu1~16.04.6), hostapd:arm64 (2:2.6-4~armbian5.35+1, 2:2.6-4~armbian5.38+1), linux-dtb-odroidc2:arm64 (5.35, 5.38), libatomic1:arm64 (5.4.0-6ubuntu1~16.04.5, 5.4.0-6ubuntu1~16.04.6), libcc1-0:arm64 (5.4.0-6ubuntu1~16.04.5, 5.4.0-6ubuntu1~16.04.6), libstdc++6:arm64 (5.4.0-6ubuntu1~16.04.5, 5.4.0-6ubuntu1~16.04.6), libstdc++6:armhf (5.4.0-6ubuntu1~16.04.5, 5.4.0-6ubuntu1~16.04.6), linux-xenial-root-odroidc2:arm64 (5.37, 5.38)