Hi, @jmarkus 
Regarding your Dell Optiplex 7010 machine - that you've upgraded from Ubuntu MATE 23.10 ("Mantic Minotaur") to Ubuntu MATE 24.04 LTS ("Noble Numbat") - and given that you mention that you can select between the Linux kernels 6.8.38 (actually, I believe that you mean 6.8.0-38 instead) and 6.5.44 (which I believe that you mean 6.5.0-44 instead), I assume that you can see the GNU GRUB (GRand Unified Bootloader) screen to select between those two kernels. Am I right? If that's the case, I suggest that you do the following:
1 - In that GRUB boot loader, select the line of the kernel that is loaded by default (I'll assume it's the line of the 6.8.0-38 kernel) and press the e key to edit the kernel options for a single boot.
2 - In the editor screen that then appears, use the arrow keys to locate the end of the line that starts with "linux "
3 - In that line, delete the words quiet splash and then press the key combination CTRL + X to boot that kernel.
If that boot works well - instead of appearing the black screen / blank screen that you've mentioned - now is the time to make that GRUB change permanent. To do that, please edit the /etc/default/grub file with administrator privileges, by running the following command (that will open the "Pluma" text editor as superuser):
sudo pluma /etc/default/grub
In that /etc/default/grub file, change the following line
GRUB_CMDLINE_LINUX_DEFAULT="quiet splash"
... change that line so it becomes the following one instead:
GRUB_CMDLINE_LINUX_DEFAULT=""
After doing that, please save and close the file, and then run the following command:
sudo update-grub
Now, please reboot the computer and see if that boot is then normal. Please reply later, in this same discussion topic, to tell us if this solved the issue for you.
I hope this helps