DELL installed a wrong mother-board on my laptop causing my windows office to not work.

The two systems are identical at the mainboard level.  The issue is likely with the activation of Microsoft 365, which can be solved by logging into your MS account and deactivating the install on the old system, and activating it on the new one (it will appear new to MS due to the mainboard change).

https://answers.microsoft.com/en-us/msoffice/forum/all/how-to-transfer-microsoft-office-365-home-to-new/f66aac4c-8b7b-457d-8112-dbb5b604b6dc

Few more points,

since my original motherboard was faulty, DELL got it replaced. In such case how can i de-activate the install on old motherboard.

My original motherboard is of VOSTRO 3500 which has 2019 MS office student & home version linked (upgraded OS to Windows 11 version now).

Replaced motherboard by mistake from DELL service is Inspiron 3501. Will the MS office version work on it??

How to get the de-activation of install on old MS system (once the new motherboard has been installed the OS & office are both re-installed, though windows is working but office is not)? When i contacted the MS support, they have said that account is fine and issue is with DELL motherboard as office account might get linked to the original motherboard and DELL should be solving it.

https://support.microsoft.com/en-au/office/deactivate-an-installation-of-office-767e3560-96ed-4b1c-806d-2fe01c529b1b