Your messages show (many times) temporary internet problems; which can be as the error message implies a temporary condition, and just waiting a bit and trying again is usually the fix.
The cause maybe many things, for me at home, power-brownouts are somewhat common and some cheap router/switches I have just die on brownout & need to be power-cycled.. It can also be my ISP is dropping my connection & I have to wait until I get a new connection using DHCP, but I don't have great internet, but very rarely there can be other network issues that aren't local too...
If I see temporary internet issues or temporary failure resolving I'll go back to basics.. Ensure my internet is up (`ip link`) that I have an ip address (`ip addr`) then I usually try and ping a few locations in the house (underhouse comms cupboard, garage where my servers are, external router) where I'm checking my internal house network (if I can't get to my comms cupboard; I'll likely get nowhere else as that's central; then I ping the 'arms' such as garage in this example AND a different 'arm' which is the router connected to my ISP or internet provider).
`ping black` is how I'd confirm my router can be reached; but that's because I have local names defined; if they weren't I'd `ping 192.168.15.4`. Assuming I had no issues to this point, I've confirmed my local networking (my home) is functional, so I test outside of the home. Note: I'm using my local network as example only; I don't know how yours is setup & hope you know. In my case almost all IP addresses are static and I know them; and not using DHCP or dynamic addresses.
On pinging external, I firstly ping my ISP using simple addresses (`ping 203.0.178.191` which I happen to know), then I ping google (`ping 8.8.8.8`). You may note I'm not using human.addresses, as I'm keeping it simple firstly & using addresses that don't require translation, sort of testing only the cable connections. If both those responded, I usually then try and ping them again using DNS or domain name service to ensure that is working, eg. `ping iinet.net.au` and `ping google.com` (not identical but close enough). If you get this far, I'd expect most internet to be working, and return & try again.
In my case, in your position, I'd firstly run `sudo apt update` and ensure all lines look correct, no warnings or missing lines etc. I may also scan my sources (ie. `/etc/apt/sources.list` and `/etc/apt/sources.list.d/ubuntu-sources` and other files in `/etc/apt/sources.list.d/`) then if all looked good, try a `sudo apt -f install` and/or `sudo apt full-upgrade`.
Your messages showed a check for a file that I see available for noble or 24.04
Code:
libglib2.0-0t64 | 2.80.0-6ubuntu1 | noble | amd64, arm64, armhf, i386, ppc64el, riscv64, s390x
libglib2.0-0t64 | 2.80.0-6ubuntu3.1 | noble-security | amd64, arm64, armhf, i386, ppc64el, riscv64, s390x
libglib2.0-0t64 | 2.80.0-6ubuntu3.1 | noble-updates | amd64, arm64, armhf, i386, ppc64el, riscv64, s390x
thus if your sources are correct; I'd expect that package to be found; and you'll note it meets the requirement I noted in your screenshot message.
As for kernels, if you get 5.15 working (you didn't specify what you've got, details can be useful) as you'd expect when selected at GRUB; you have useful knowledge.
Can you use a text terminal; ie. let the system boot, and when it appears 'stuck', can you switch to a text terminal using Ctrl+Alt+F4 for example?
If booting an older 5.15 kernel however responds the same as your 6.8 kernel; I'd try and boot the system only to runlevel 1 (ie. I'll edit grub line and add a ' 1 ' to the linux kernel line) and manually boot system from there (I'd also likely remove 'quiet splash' too, so I'm seeing more messages that may provide clues). What I'm looking for here is that the system boots; I'd also try this on the newer 6.8 kernel... as if it looks good from here, especially if you're getting text terminal logins - your issue is GUI only related... and package commands from text terminal is likely how I'd fix that.
Sorry this won't be easy to follow I realize, hopefully you've gained something useful anyway.