You might be able to, but I wouldn't recommend it. You may have trouble with proprietary front panel connectors or the PSU if you intend to re use that, too. An aftermarket case would be easier to build into and you avoid problems with the connectors and clearances for certain parts such as the PSU, CPU cooler and graphics card.
A couple other things to consider are the motherboard mounting and the front panel USB ports. If that PC used a proprietary motherboard, the standoff's may have a pattern that won't work with aftermarket boards and the USB ports will be limited to USB 1.0 or 2.0 (whatever they are) and not the 3.0 found on modern motherboards.