This incident had occurred a few days ago as well but then on another restart, it was fixed.
That should have been your cue to backup all your data
then. It is very rare for a drive that exhibits such problems to get "fixed" on any sort of permanent basis - especially with just a reboot. Such a "sign" is typically just an indicator of more problems to come, and eventual doom - and despair if no backup.
Clicking noises from a drive typically indicated the R/W heads are banging against the end-stops, searching for a non-corrupt boot sector. And screeching is typically bearings, or the R/W head cutting Grand Canyon size (microscopically speaking) gouges in the platters. Either way, not good.
As you have discovered, you can connect a notebook HD to another computer. This can be done in many ways from direct cable connection, to installing the drive into an enclosure or docking station connected via USB. As long as the drive is not connected in the boot position, no problems.
From here, you can try a data recovery program to see if anything is recoverable. I use and recommend
Recuva from the makers of CCleaner. But if the drive is not even recognized by the system (BIOS/Chipset), no software recovery program will help. And then your only recourse is to take the drive to a data recovery service where they will break down the drive and analyze the platters for any recoverable data using very sophisticated (read: expensive!!!) equipment. These services can cost from several $100, to several $1000!
Only you can put a value on your data.
Sorry I don't have more encouraging news.
EVERYONE should heed this warning, "
ALL drives WILL FAIL - eventually!" Create a viable backup now, and regularly there after.