I have a multi-boot machine with a Ubuntu 14 partition, an ubuntu 16 partition and a Windows partition (probably Windows 10). I hadn't used Windows in over a year and after rebooting, it forced me into Windows updates. After that, my machine won't reboot. I get to the GRUB rescue prompt. The only error message is
error: no such partition
I could not run any useful commands from the GRUB rescue prompt, so I removed the hard disk and mounted it on a separate Ubuntu PC. I ran parted on the disk and this is what it looks like:
Disk /dev/sdb: 2000GB
Sector size (logical/physical): 512B/4096B
Partition Table: msdos
Disk Flags: 
Number  Start   End     Size    Type      File system     Flags
 1      1049kB  525MB   524MB   primary   ntfs            boot
 2      525MB   1015GB  1014GB  primary   ntfs
 3      1015GB  1015GB  891MB   primary   ntfs            diag
 4      1015GB  2000GB  985GB   extended
 5      1983GB  2000GB  17.1GB  logical   linux-swap(v1)
I want to fix grub so it can multi-boot Windows (Partition 2), Ubuntu 14 and Ubuntu 16. I don't remember how I created the Ubuntu partitions, but I'm hoping they are somewhere in the extended partition 4 (maybe they are logical volumes?). Can I do this?
UPDATE: I was able to recover the two Ubuntu partitions with testdisk. I then rebooted into Ubuntu 14 via grub rescue mode. I think the hard part is done. Now, I have to get grub working correctly. Currently, this is what I have to do in order to get to the grub boot menu:
    set root=(hd0,msdos5)
    set prefix=(hd0,msdos5)/boot/grub
    insmod normal
    normal
How can I fix things so that grubs runs without having to go through the grub rescue prompt? Possibly load grub into the Master Boot Record?
 
    