Hello, I’m Virginia, a fellow user like yourself.
Sorry to hear you’re experiencing problems. May I ask which Windows 11 build are you running - 21H2 or 22H2?
Did Windows come pre-installed on the pc or was it purchased separately? If it was pre-installed then it would be OEM & this 'died' with the Motherboard. If Dell replaced the Motherboard then they may need to supply a new key/license.
If Retail then there are a few things you can try. I understand you've tried some things so I apologise if I suggest things which you've already done.
Are you using any third party antivirus software or VPN? if yes then disable this or even better uninstall it using the developer's removal tool & try activating again.
Have you checked to see if you can download updates &/or apps from the Store? if this also fails then let me know. Can you access the Internet OK or does this fail too?
Have you tried entering the default Windows key? Home/Core: YTMG3-N6DKC-DKB77-7M9GH-8HVX7
Are you connected to the internet via Wi-Fi or Ethernet? If Wi-Fi can you try Ethernet? Have you reset the network settings?
Start>Settings>Network & Internet>Advanced Network settings>Click Reset Network.
Ensure Ethernet's TCP/IP is set to Automatic.