There's a possibility that the motherboard is a proprietary form factor, or at least has proprietary mounting holes, which would mean it's impossible to move it to a new case. If you do still want to move into a new case and need a new motherboard, you'll probably have to buy used based on the age of the CPU. But unfortunately, changing motherboards is probably the most laborious component to change. Changing motherboards will greatly interfere with your OS installation, so you'll either need to do a new OS install or you'll need to do an OS migration before the computer will even boot to desktop. There's a few different software solutions to do that. Fresh install or migrated install, you'll need to reactivate your OS, as well.
The...