Don't give up
I had a similar problem with an old desktop computer running Ubuntu 22.04. The upgrade to 24.04 left me with a black screen with a blinking cursor.
Open a virtual terminal
If the desktop GUI is not available open a virtual terminal (What is a virtual terminal for?) by pressing Ctrl+Alt+F2.
I used the following commands:
sudo dpkg --configure -a
sudo apt --fix-broken install
sudo apt full-upgrade
sudo reboot
Then I went back to the virtual terminal and used:
sudo apt install ubuntu-desktop
sudo reboot
In the Desktop GUI
I was able to get the GUI back after this. I opened the Software Updater app and started a partial upgrade. When the partial upgrade was complete, I rebooted the computer again.
Note the PPAs are disabled as a part of the upgrade process. You can enable the disabled PPAs from the app Software & Updater's Other Software tab. When you enable the disabled PPAs, you will have to replace focal with noble where needed. Some PPAs may not work if they don't have a version for noble (24.04).
Internet or server side problems:
One of the errors you have reported indicate a possibily unrelated problem:
3 Err:2 http://archive.ubuntu.com/ubuntu noble-updates InRelease
Temporary failure resolving "archive.ubuntu.com"
This indicates one of the three conditions:
- The repository server "archive.ubuntu.com" is offline
- There is a DNS resolution problem either in your computer or in your router
- Your computer does not have Internet connection
The first of these three can happen if the server is overwhelmed with many people trying to upgrade at the same time. Try again later.
If nothing works
Use a different computer to download and create a live installation USB drive for Ubuntu 24.04. Then follow these steps on the problem computer:
- Boot the computer using the Live installation USB and select the Try Ubuntu option. Do not select the "Install" option at this stage.
- Get an external hard drive and copy the contents of your Home folder in the external hard drive. It is best if the external hard drive has an ext4 partition. This will ensure all the ownership and permissions of the files and folders in the "Home" folder is preserved. However, this is not essential for documents, pictures, etc.
- Install Ubuntu erasing everything (assuming you don't have Windows).
- Reboot to newly installed Ubuntu 24.04 and copy the files back from
the external hard drive.
Hope this helps