Partly.
Updated a system for a friend using dosdudes unofficial installers (
http://dosdude1.com/software.html ) a while ago -
- You can extract the bootable image used to create a bootdrive, from an update at least in more recent versions, and then make a bootable usb drive
- The update I looked for in particular (and in the end downloaded from Apple and used) had a different checksum, than the ones shared on the net, so those updates might be region dependent (or not - never found out)
- All of dosdudes installers come with a routine, that pulls the necessary files from Apples source servers, and compiles them into a fully working update - for that version (so every dosdude installer has a routine in it that can produce (download) the most recent update for that MacOs version (the one in the title of the respective dosdude updater), with just 2-3 mouse clicks)
- Updates in place usually work well on Macs, so if you go with the latest version of 10.9 (didnt check if you already did) - you should be fine also
Issue - the dosdude installers start with 10.12 so - no luck there.
For fixing, I would try to stick to your method, trying to acquire 10.9 first -- even if the unofficial installers from dosdude work on your model - because somewhere in there is a filesystem switch dosdude has to perform for newer versions of Mac OS, so some risk of data loss - which is why getting the system up and running first - and then making a backup before trying might be better.
If data loss doesnt matter, and the laptop is on dosdudes compatibility list - read into the unofficial updaters - if they work in your case, they are probably the way to go anyhow - longterm. (There are also a few youtube videos on the topic, not the best ones, ... reading up on the installers still is preferable, but they are there...)
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I can say for sure, that there is a way to download and build updates (and therefore installers - ("therefore" at least on newer OS versions, dont know for sure that this also goes for maverick)) from Apples Build servers -
aside from the routine that is in dosdudes tools that can do that from Sierra onwards, you can also try using this:
https://github.com/corpnewt/gibMacOS
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If everything fails, before resorting to torrenting, probably try phoning local third party Mac repair shops, they are bound to have the install media - for sure.
Before you start torrenting. Imho.
edit: Oh - and on the official "update download servers" Apple provides (not sure if you need a free dev account or not), they only host incremental updates - for older MacOS versions, so if you want to download the full update/installer from apple, you need to go with a script/routine, that can compile the update from individual packages, apple hosts online to this day - for older versions.