Computer crashed during pacman -Syu and manjaro is now unbootable. How can I recover files in my home directory?

[omano]

Just chroot your installation, rerun the update to see if it fixes it.

[HowTo] Recovering from an interrupted update/upgrade

Difficulty: ★★☆☆☆ So you couldn’t wait until the update process had completed and you went for the reset/power button, didn’t you? And now you’re getting the message that you don’t have a kernel installed. Well, you’re not the only one — we’re seeing it happen all the time. So, here’s how to fix it, you impatient n00b. If you don’t happen to have a recent Manjaro installer USB/DVD/CD handy, direct your browser to this wonderful page, download t…

Make a proper Manjaro USB, it will show up in your boot menu if you create it correctly. Or you disabled USB in your motherboard which would be very unlikely.