Cannot Find BaseSystem.dmg For iMac SSD Replacment

The simplest option would be to get the old hard drive back and boot from it so you can create a bootable macOS 10.11 El Capitan USB installer.

Create a bootable installer for macOS (includes link to download installers) - Apple Support

The other option would be to get the OS X 10.6 Snow Leopard Upgrade DVD and start from there & then upgrade to macOS 10.11 El Capitan.

Or install Linux Mint onto the new SSD which would give you are current non-Apple OS with access to the current versions of the popular web browsers (Firefox, Vivaldi, Chrome, etc.) and lots of free open source software such as LibreOffice. This does require you to learn a new OS. Linux is not for everyone though,, but it is a great way to extend the useful life of an older computer. You can even check out what it is like by selecting the "Live" option when booting the Linux Mint USB installer although it will run extremely slow from the USB stick (it will run much better when installed onto the internal SSD).

10.11.6 is the highest you can install o a 2008 iMac.

Use a web browser for older versions

These older macOS versions are available as disk images that you can download using your web browser. To get the installer from the disk image, you must use a Mac that is compatible with that macOS.

1. Use these links to download a macOS disk image (.dmg) file. If these links don't work as expected, try again using Safari, which is in your Applications folder.

• • Sierra 10.12
  • El Capitan 10.11
  • Yosemite 10.10
  • Mountain Lion 10.8
  • Lion 10.7

1. Double-click the .dmg file to open it and see the package (.pkg) file within.
2. Double-click the .pkg file, then follow the onscreen instructions to install the macOS installer into your Applications folder.
3. Open your Applications folder and double-click the macOS installer, named Install [Version Name]. Follow the onscreen installation instructions.

Use a bootable installer

A bootable installer can be useful if you want to install macOS on multiple computers without downloading the installer each time, or when you can't install using macOS Recovery or the other methods.

To download an installer suitable for creating a bootable installer, use the App Store or use a web browser to download from a compatible Mac. The Mac must also be using macOS High Sierra or later, the latest version of macOS Sierra, or the latest version of OS X El Capitan.

How to create a bootable installer for macOS

After replacing its boot disk you will need to boot from that iMac's original, grey, System Install DVD so that you can install an operating system. Those two grey discs must accompany the Macs that shipped with them from cradle to grave.

Other options include HWTech's suggestions.

That Mac is too old for OS X Recovery.

If you're using a wireless KB you may need to use a cheap USB KB & Mouse...

https://www.amazon.com/dp/B00B7GV802?

Windows Win key = Mac CMD key or ⌘ 

Windows alt key = Mac Option key or ⌥, also called alt key on Mac sometimes.

I'm having software problems in my MacBoo… - Apple Community

You cannot write or save to High Sierra BaseSystem.

You say Formatted correctly, but...

In Disk Utility>View, select Show all Devices, highlight the top left entry.

What does it say?

Can you upload a pic of the screen?

Installing Linux on an older laptop - Apple Community

https://lerhonewalker.com/thoughts/tech-upcycle-running-ubuntu-linux-on-a-2007-imac/

Sorry, besides Just needing a screenshot where I ca read the text... I just do not have the Data & Bandwidth for videos... sorry.

Yes. Those two discs will simplify your options considerably. Make every effort to find them.