I'm going to install a new motherboard in a damaged Dell Optiplex 740 and I was wondering if I install the mobo in the same way the damaged one was and not changed anything else, will I still have to reinstall Windows or will it boot and run as it did with the old mobo?
If you use an exact replacement Dell motherboard it will work OK. If you use a different motherboard then you have a "different" PC and the Dell OEM OS is no longer legally valid. It is only valid for the PC it was delivered with, or an exact replacement (but you will probably have to activate it with Microsoft).
Another issue, Dells, generally, do not support (fit) non-Dell motherboards (or motherboards for other Dell models). The motherboard mounting holes can be different and the back panel I/O panel on many cases is solid and not an insert like a standard ATX case.
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