Recent OS update did not go well

Did you try it more than once? If so then you need to start by using a Snow Leopard installer DVD that came with your computer when it was new.

Snow Leopard Erase and Install

1. Insert the Snow Leopard DVD into the optical drive and restart the computer.
2. Immediately upon hearing the chime hold down the C key.
3. Release the key when the Apple logo appears and wait for the loading to finish.
4. After the installer loads select your language and click on the Continue button. When the menu bar appears select Disk Utility from the Utilities' menu. After Disk Utility loads select the out-dented disk entry from the side list (mfgr.'s ID and drive size.) Click on the Partition tab in the Disk Utility’s right window. Set the number of partitions to one (1) from the drop down menu. Click on the Options button and select GUID, click OK button, set the format type to MacOS Extended, Journaled. Finally, click on the Apply button.
5. After formatting has finished quit Disk Utility. Continue with the OS X installation and follow the directions.
6. When the installation has finished the computer will restart into the Setup Assistant. After you complete the Setup Assistant you will be running a fresh installation of Snow Leopard. Open Software Update and install the recommended updates.
7. If you are planning to sell or give your computer away, then do the following: After you reformat your hard drive and reinstall Snow Leopard, the computer restarts to a Welcome screen. To leave the Mac in an OOTB (Out Of The Box) state, don't continue with the setup. Instead, press Command and Q keys to shut down the computer. The Setup Assistant will guide the new owner through the setup process after he/she turns on the computer.
8. Download and install Mac OS X 10.6.8 Update Combo v1.1. if needed. It is not needed if you are selling or giving away the computer.
9. Connect to the App Store and download the required version of macOS - How to download macOS High Sierra.

Unfortunately, you cannot use the only retail version, Snow Leopard 10.6.3, because your model requires a special version never sold publicly. The only source is to call Apple Support and see if they have copies for sale. Your model is obsolete so they may no longer have copies to sell. It is a two disk set. You used to be able to buy Lion on a bootable disk or USB flash drive. I think it could be installed directly without having to install Snow Leopard.

Upgrading to Lion

You can purchase Lion at the Online Apple Store. The cost is $19.99 (as it was before) plus tax. It's a download. You will get an email containing a redemption code that you then use at the Mac App Store to download Lion. Save a copy of that installer to your Downloads folder because the installer deletes itself at the end of the installation.

Lion System Requirements

1. Mac computer with an Intel Core 2 Duo, Core i3, Core i5, Core i7,

or Xeon processor

2. 2GB of memory

3. OS X v10.6.6 or later (v10.6.8 recommended)

4. 7GB of available space

5. Some features require an Apple ID; terms apply.

Are my applications compatible? See App Compatibility Table - RoaringApps.

Try this:

Install El Capitan or Later from Scratch

If possible backup your files.

1. Restart the computer. Immediately after the chime hold down the CommandandRkeys until the Apple logo appears. When the Utility Menu appears:
2. Select Disk Utility from the Utility Menu and click on Continue button.
3. When Disk Utility loads select the volume (indented entry, usually Macintosh HD) from the Device list.
4. Click on the Erase icon in Disk Utility's main window. A panel will drop down.
5. Set the Format type to APFS (SSDs only) or Mac OS Extended (Journaled.)
6. Click on the Apply button, then wait for the Done button to activate and click on it.
7. Quit Disk Utility and return to the Utility Menu.
8. Select Install OS X and click on the Continue button.

This will install the version of OS X you had installed.